linear_algebra.orientation ⟷ Mathlib.LinearAlgebra.Orientation

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

@@ -293,7 +293,7 @@ theorem eq_or_eq_neg_of_isEmpty [Nontrivial R] [IsEmpty ι] (o : Orientation R M
     convert h.map' (↑alternating_map.const_linear_equiv_of_is_empty.symm) (LinearEquiv.ker _)
     ext i
     fin_cases i <;> simp [a]
-  rw [linearIndependent_iff'] at H 
+  rw [linearIndependent_iff'] at H
   simpa using H Finset.univ ![1, -a] (by simp [Fin.sum_univ_succ]) 0 (by simp)
 #align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmpty
 -/
@@ -322,7 +322,7 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.Orientation ∨ x = -e.Orientation :=
   by
   induction' x using Module.Ray.ind with x hx
-  rw [← x.map_basis_ne_zero_iff e] at hx 
+  rw [← x.map_basis_ne_zero_iff e] at hx
   rwa [Basis.orientation, ray_eq_iff, neg_rayOfNeZero, ray_eq_iff, x.eq_smul_basis_det e,
     sameRay_neg_smul_left_iff_of_ne e.det_ne_zero hx, sameRay_smul_left_iff_of_ne e.det_ne_zero hx,
     lt_or_lt_iff_ne, ne_comm]

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

@@ -493,7 +493,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   cases isEmpty_or_nonempty ι
   · have H : finrank R M = 0 := by
       refine' h.symm.trans _
-      convert Fintype.card_of_isEmpty
+      convert Fintype.card_ofIsEmpty
       infer_instance
     simp [LinearMap.det_eq_one_of_finrank_eq_zero H]
   have H : 0 < finrank R M := by
@@ -514,7 +514,7 @@ theorem map_eq_neg_iff_det_neg (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   cases isEmpty_or_nonempty ι
   · have H : finrank R M = 0 := by
       refine' h.symm.trans _
-      convert Fintype.card_of_isEmpty
+      convert Fintype.card_ofIsEmpty
       infer_instance
     simp [LinearMap.det_eq_one_of_finrank_eq_zero H, Module.Ray.ne_neg_self x]
   have H : 0 < finrank R M := by

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

@@ -108,7 +108,7 @@ variable (R M) {ι ι'}
 #print Orientation.reindex /-
 /-- An equivalence between indices implies an equivalence between orientations. -/
 def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R M ι' :=
-  Module.Ray.map <| AlternatingMap.domDomLcongr R e
+  Module.Ray.map <| AlternatingMap.domDomCongrₗ R e
 #align orientation.reindex Orientation.reindex
 -/
 
@@ -124,7 +124,7 @@ theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι)
 #print Orientation.reindex_refl /-
 @[simp]
 theorem Orientation.reindex_refl : (Orientation.reindex R M <| Equiv.refl ι) = Equiv.refl _ := by
-  rw [Orientation.reindex, AlternatingMap.domDomLcongr_refl, Module.Ray.map_refl]
+  rw [Orientation.reindex, AlternatingMap.domDomCongrₗ_refl, Module.Ray.map_refl]
 #align orientation.reindex_refl Orientation.reindex_refl
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.LinearAlgebra.Ray
-import Mathbin.LinearAlgebra.Determinant
+import LinearAlgebra.Ray
+import LinearAlgebra.Determinant
 
 #align_import linear_algebra.orientation from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -105,28 +105,36 @@ section Reindex
 
 variable (R M) {ι ι'}
 
+#print Orientation.reindex /-
 /-- An equivalence between indices implies an equivalence between orientations. -/
 def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R M ι' :=
   Module.Ray.map <| AlternatingMap.domDomLcongr R e
 #align orientation.reindex Orientation.reindex
+-/
 
+#print Orientation.reindex_apply /-
 @[simp]
 theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
     Orientation.reindex R M e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.domDomCongr e) (mt (v.domDomCongr_eq_zero_iff e).mp hv) :=
   rfl
 #align orientation.reindex_apply Orientation.reindex_apply
+-/
 
+#print Orientation.reindex_refl /-
 @[simp]
 theorem Orientation.reindex_refl : (Orientation.reindex R M <| Equiv.refl ι) = Equiv.refl _ := by
   rw [Orientation.reindex, AlternatingMap.domDomLcongr_refl, Module.Ray.map_refl]
 #align orientation.reindex_refl Orientation.reindex_refl
+-/
 
+#print Orientation.reindex_symm /-
 @[simp]
 theorem Orientation.reindex_symm (e : ι ≃ ι') :
     (Orientation.reindex R M e).symm = Orientation.reindex R M e.symm :=
   rfl
 #align orientation.reindex_symm Orientation.reindex_symm
+-/
 
 end Reindex
 
@@ -177,11 +185,13 @@ protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Ori
 #align orientation.map_neg Orientation.map_neg
 -/
 
+#print Orientation.reindex_neg /-
 @[simp]
 protected theorem Orientation.reindex_neg {ι ι' : Type _} (e : ι ≃ ι') (x : Orientation R M ι) :
     Orientation.reindex R M e (-x) = -Orientation.reindex R M e x :=
   Module.Ray.map_neg _ x
 #align orientation.reindex_neg Orientation.reindex_neg
+-/
 
 namespace Basis
 
@@ -219,10 +229,12 @@ theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
 #align basis.orientation_map Basis.orientation_map
 -/
 
+#print Basis.orientation_reindex /-
 theorem orientation_reindex [Nontrivial R] (e : Basis ι R M) (eι : ι ≃ ι') :
     (e.reindex eι).Orientation = Orientation.reindex R M eι e.Orientation := by
   simp_rw [Basis.orientation, Orientation.reindex_apply, Basis.det_reindex']
 #align basis.orientation_reindex Basis.orientation_reindex
+-/
 
 #print Basis.orientation_unitsSMul /-
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -6,7 +6,7 @@ Authors: Joseph Myers
 import Mathbin.LinearAlgebra.Ray
 import Mathbin.LinearAlgebra.Determinant
 
-#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
+#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
 /-!
 # Orientations of modules
@@ -49,7 +49,7 @@ variable (M : Type _) [AddCommMonoid M] [Module R M]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
-variable (ι : Type _)
+variable (ι ι' : Type _)
 
 #print Orientation /-
 /-- An orientation of a module, intended to be used when `ι` is a `fintype` with the same
@@ -101,6 +101,35 @@ theorem Orientation.map_symm (e : M ≃ₗ[R] N) :
 #align orientation.map_symm Orientation.map_symm
 -/
 
+section Reindex
+
+variable (R M) {ι ι'}
+
+/-- An equivalence between indices implies an equivalence between orientations. -/
+def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R M ι' :=
+  Module.Ray.map <| AlternatingMap.domDomLcongr R e
+#align orientation.reindex Orientation.reindex
+
+@[simp]
+theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
+    Orientation.reindex R M e (rayOfNeZero _ v hv) =
+      rayOfNeZero _ (v.domDomCongr e) (mt (v.domDomCongr_eq_zero_iff e).mp hv) :=
+  rfl
+#align orientation.reindex_apply Orientation.reindex_apply
+
+@[simp]
+theorem Orientation.reindex_refl : (Orientation.reindex R M <| Equiv.refl ι) = Equiv.refl _ := by
+  rw [Orientation.reindex, AlternatingMap.domDomLcongr_refl, Module.Ray.map_refl]
+#align orientation.reindex_refl Orientation.reindex_refl
+
+@[simp]
+theorem Orientation.reindex_symm (e : ι ≃ ι') :
+    (Orientation.reindex R M e).symm = Orientation.reindex R M e.symm :=
+  rfl
+#align orientation.reindex_symm Orientation.reindex_symm
+
+end Reindex
+
 #print IsEmpty.oriented /-
 /-- A module is canonically oriented with respect to an empty index type. -/
 instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι
@@ -148,9 +177,15 @@ protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Ori
 #align orientation.map_neg Orientation.map_neg
 -/
 
+@[simp]
+protected theorem Orientation.reindex_neg {ι ι' : Type _} (e : ι ≃ ι') (x : Orientation R M ι) :
+    Orientation.reindex R M e (-x) = -Orientation.reindex R M e x :=
+  Module.Ray.map_neg _ x
+#align orientation.reindex_neg Orientation.reindex_neg
+
 namespace Basis
 
-variable {ι : Type _}
+variable {ι ι' : Type _}
 
 #print Basis.map_orientation_eq_det_inv_smul /-
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
@@ -168,7 +203,7 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
 #align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smul
 -/
 
-variable [Fintype ι] [DecidableEq ι]
+variable [Fintype ι] [DecidableEq ι] [Fintype ι'] [DecidableEq ι']
 
 #print Basis.orientation /-
 /-- The orientation given by a basis. -/
@@ -184,6 +219,11 @@ theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
 #align basis.orientation_map Basis.orientation_map
 -/
 
+theorem orientation_reindex [Nontrivial R] (e : Basis ι R M) (eι : ι ≃ ι') :
+    (e.reindex eι).Orientation = Orientation.reindex R M eι e.Orientation := by
+  simp_rw [Basis.orientation, Orientation.reindex_apply, Basis.det_reindex']
+#align basis.orientation_reindex Basis.orientation_reindex
+
 #print Basis.orientation_unitsSMul /-
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.orientation
-! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Ray
 import Mathbin.LinearAlgebra.Determinant
 
+#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
+
 /-!
 # Orientations of modules
 

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

@@ -80,23 +80,29 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 #align orientation.map Orientation.map
 -/
 
+#print Orientation.map_apply /-
 @[simp]
 theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
     Orientation.map ι e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.compLinearMap e.symm) (mt (v.comp_linearEquiv_eq_zero_iff e.symm).mp hv) :=
   rfl
 #align orientation.map_apply Orientation.map_apply
+-/
 
+#print Orientation.map_refl /-
 @[simp]
 theorem Orientation.map_refl : (Orientation.map ι <| LinearEquiv.refl R M) = Equiv.refl _ := by
   rw [Orientation.map, AlternatingMap.domLCongr_refl, Module.Ray.map_refl]
 #align orientation.map_refl Orientation.map_refl
+-/
 
+#print Orientation.map_symm /-
 @[simp]
 theorem Orientation.map_symm (e : M ≃ₗ[R] N) :
     (Orientation.map ι e).symm = Orientation.map ι e.symm :=
   rfl
 #align orientation.map_symm Orientation.map_symm
+-/
 
 #print IsEmpty.oriented /-
 /-- A module is canonically oriented with respect to an empty index type. -/
@@ -107,12 +113,15 @@ instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module
 #align is_empty.oriented IsEmpty.oriented
 -/
 
+#print Orientation.map_positiveOrientation_of_isEmpty /-
 @[simp]
 theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty ι] (f : M ≃ₗ[R] N) :
     Orientation.map ι f positiveOrientation = positiveOrientation :=
   rfl
 #align orientation.map_positive_orientation_of_is_empty Orientation.map_positiveOrientation_of_isEmpty
+-/
 
+#print Orientation.map_of_isEmpty /-
 @[simp]
 theorem Orientation.map_of_isEmpty [IsEmpty ι] (x : Orientation R M ι) (f : M ≃ₗ[R] M) :
     Orientation.map ι f x = x :=
@@ -124,6 +133,7 @@ theorem Orientation.map_of_isEmpty [IsEmpty ι] (x : Orientation R M ι) (f : M
   rw [AlternatingMap.compLinearMap_apply]
   congr
 #align orientation.map_of_is_empty Orientation.map_of_isEmpty
+-/
 
 end OrderedCommSemiring
 
@@ -133,16 +143,19 @@ variable {R : Type _} [StrictOrderedCommRing R]
 
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
+#print Orientation.map_neg /-
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
     Orientation.map ι f (-x) = -Orientation.map ι f x :=
   Module.Ray.map_neg _ x
 #align orientation.map_neg Orientation.map_neg
+-/
 
 namespace Basis
 
 variable {ι : Type _}
 
+#print Basis.map_orientation_eq_det_inv_smul /-
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
 theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orientation R M ι)
@@ -156,6 +169,7 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
     AlternatingMap.compLinearMap_apply, AlternatingMap.smul_apply, Basis.det_comp, Basis.det_self,
     mul_one, smul_eq_mul, mul_comm, mul_smul, LinearEquiv.coe_inv_det]
 #align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smul
+-/
 
 variable [Fintype ι] [DecidableEq ι]
 
@@ -166,11 +180,14 @@ protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι
 #align basis.orientation Basis.orientation
 -/
 
+#print Basis.orientation_map /-
 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).Orientation = Orientation.map ι f e.Orientation := by
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
 #align basis.orientation_map Basis.orientation_map
+-/
 
+#print Basis.orientation_unitsSMul /-
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
 theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
@@ -181,8 +198,10 @@ theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
   norm_cast
   simp
 #align basis.orientation_units_smul Basis.orientation_unitsSMul
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
+#print Basis.orientation_isEmpty /-
 @[simp]
 theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
     b.Orientation = positiveOrientation :=
@@ -191,6 +210,7 @@ theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]]"
   convert b.det_is_empty
 #align basis.orientation_is_empty Basis.orientation_isEmpty
+-/
 
 end Basis
 
@@ -206,6 +226,7 @@ variable {ι : Type _}
 
 namespace Orientation
 
+#print Orientation.eq_or_eq_neg_of_isEmpty /-
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
 mathematical sense if `M` is zero-dimensional.) -/
@@ -226,6 +247,7 @@ theorem eq_or_eq_neg_of_isEmpty [Nontrivial R] [IsEmpty ι] (o : Orientation R M
   rw [linearIndependent_iff'] at H 
   simpa using H Finset.univ ![1, -a] (by simp [Fin.sum_univ_succ]) 0 (by simp)
 #align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmpty
+-/
 
 end Orientation
 
@@ -233,6 +255,7 @@ namespace Basis
 
 variable [Fintype ι] [DecidableEq ι]
 
+#print Basis.orientation_eq_iff_det_pos /-
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
 theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
@@ -242,7 +265,9 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
     _ ↔ SameRay R (e₁.det e₂ • e₂.det) e₂.det := by rw [← e₁.det.eq_smul_basis_det e₂]
     _ ↔ 0 < e₁.det e₂ := sameRay_smul_left_iff_of_ne e₂.det_ne_zero (e₁.isUnit_det e₂).NeZero
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
+-/
 
+#print Basis.orientation_eq_or_eq_neg /-
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/
 theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.Orientation ∨ x = -e.Orientation :=
@@ -253,7 +278,9 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     sameRay_neg_smul_left_iff_of_ne e.det_ne_zero hx, sameRay_smul_left_iff_of_ne e.det_ne_zero hx,
     lt_or_lt_iff_ne, ne_comm]
 #align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_neg
+-/
 
+#print Basis.orientation_ne_iff_eq_neg /-
 /-- Given a basis, an orientation equals the negation of that given by that basis if and only
 if it does not equal that given by that basis. -/
 theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
@@ -261,7 +288,9 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
   ⟨fun h => (e.orientation_eq_or_eq_neg x).resolve_left h, fun h =>
     h.symm ▸ (Module.Ray.ne_neg_self e.Orientation).symm⟩
 #align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_neg
+-/
 
+#print Basis.orientation_comp_linearEquiv_eq_iff_det_pos /-
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
 theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -269,7 +298,9 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
   rw [orientation_map, e.map_orientation_eq_det_inv_smul, units_inv_smul, units_smul_eq_self_iff,
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_pos
+-/
 
+#print Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg /-
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
 theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -277,7 +308,9 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
   rw [orientation_map, e.map_orientation_eq_det_inv_smul, units_inv_smul, units_smul_eq_neg_iff,
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg
+-/
 
+#print Basis.orientation_neg_single /-
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
 @[simp]
@@ -287,6 +320,7 @@ theorem orientation_neg_single [Nontrivial R] (e : Basis ι R M) (i : ι) :
   rw [orientation_units_smul, Finset.prod_update_of_mem (Finset.mem_univ _)]
   simp
 #align basis.orientation_neg_single Basis.orientation_neg_single
+-/
 
 #print Basis.adjustToOrientation /-
 /-- Given a basis and an orientation, return a basis giving that orientation: either the original
@@ -298,6 +332,7 @@ def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Ori
 #align basis.adjust_to_orientation Basis.adjustToOrientation
 -/
 
+#print Basis.orientation_adjustToOrientation /-
 /-- `adjust_to_orientation` gives a basis with the required orientation. -/
 @[simp]
 theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -309,7 +344,9 @@ theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis
   · rw [orientation_neg_single, eq_comm, ← orientation_ne_iff_eq_neg, ne_comm]
     exact h
 #align basis.orientation_adjust_to_orientation Basis.orientation_adjustToOrientation
+-/
 
+#print Basis.adjustToOrientation_apply_eq_or_eq_neg /-
 /-- Every basis vector from `adjust_to_orientation` is either that from the original basis or its
 negation. -/
 theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -321,7 +358,9 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
   · simp
   · by_cases hi : i = Classical.arbitrary ι <;> simp [units_smul_apply, hi]
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
+-/
 
+#print Basis.det_adjustToOrientation /-
 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
     (e.adjustToOrientation x).det = e.det ∨ (e.adjustToOrientation x).det = -e.det :=
@@ -333,12 +372,15 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
   · right
     simp [e.det_units_smul, ← Units.coe_prod, Finset.prod_update_of_mem]
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
+-/
 
+#print Basis.abs_det_adjustToOrientation /-
 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (v : ι → M) : |(e.adjustToOrientation x).det v| = |e.det v| := by
   cases' e.det_adjust_to_orientation x with h h <;> simp [h]
 #align basis.abs_det_adjust_to_orientation Basis.abs_det_adjustToOrientation
+-/
 
 end Basis
 
@@ -358,8 +400,7 @@ variable [Fintype ι] [_i : FiniteDimensional R M]
 
 open FiniteDimensional
 
-include _i
-
+#print Orientation.eq_or_eq_neg /-
 /-- If the index type has cardinality equal to the finite dimension, any two orientations are
 equal or negations. -/
 theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -371,7 +412,9 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
       rcases e.orientation_eq_or_eq_neg x₂ with (h₂ | h₂) <;>
     simp [h₁, h₂]
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg
+-/
 
+#print Orientation.ne_iff_eq_neg /-
 /-- If the index type has cardinality equal to the finite dimension, an orientation equals the
 negation of another orientation if and only if they are not equal. -/
 theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -379,7 +422,9 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
   ⟨fun hn => (eq_or_eq_neg x₁ x₂ h).resolve_left hn, fun he =>
     he.symm ▸ (Module.Ray.ne_neg_self x₂).symm⟩
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
+-/
 
+#print Orientation.map_eq_det_inv_smul /-
 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
 theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
@@ -387,9 +432,9 @@ theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   haveI e := (fin_basis R M).reindex (Fintype.equivFinOfCardEq h).symm
   e.map_orientation_eq_det_inv_smul x f
 #align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smul
+-/
 
-omit _i
-
+#print Orientation.map_eq_iff_det_pos /-
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
 determinant is positive. -/
@@ -408,7 +453,9 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   haveI : FiniteDimensional R M := finite_dimensional_of_finrank H
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_self_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
+-/
 
+#print Orientation.map_eq_neg_iff_det_neg /-
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and
 only if the determinant is negative. -/
@@ -427,8 +474,7 @@ theorem map_eq_neg_iff_det_neg (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   haveI : FiniteDimensional R M := finite_dimensional_of_finrank H
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_neg_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_neg
-
-include _i
+-/
 
 #print Orientation.someBasis /-
 /-- If the index type has cardinality equal to the finite dimension, a basis with the given
@@ -439,12 +485,14 @@ def someBasis [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
 #align orientation.some_basis Orientation.someBasis
 -/
 
+#print Orientation.someBasis_orientation /-
 /-- `some_basis` gives a basis with the required orientation. -/
 @[simp]
 theorem someBasis_orientation [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
     (h : Fintype.card ι = finrank R M) : (x.someBasis h).Orientation = x :=
   Basis.orientation_adjustToOrientation _ _
 #align orientation.some_basis_orientation Orientation.someBasis_orientation
+-/
 
 end Orientation
 

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

@@ -241,7 +241,6 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
     e₁.Orientation = e₂.Orientation ↔ SameRay R e₁.det e₂.det := ray_eq_iff _ _
     _ ↔ SameRay R (e₁.det e₂ • e₂.det) e₂.det := by rw [← e₁.det.eq_smul_basis_det e₂]
     _ ↔ 0 < e₁.det e₂ := sameRay_smul_left_iff_of_ne e₂.det_ne_zero (e₁.isUnit_det e₂).NeZero
-    
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
 
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/

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

@@ -223,7 +223,7 @@ theorem eq_or_eq_neg_of_isEmpty [Nontrivial R] [IsEmpty ι] (o : Orientation R M
     convert h.map' (↑alternating_map.const_linear_equiv_of_is_empty.symm) (LinearEquiv.ker _)
     ext i
     fin_cases i <;> simp [a]
-  rw [linearIndependent_iff'] at H
+  rw [linearIndependent_iff'] at H 
   simpa using H Finset.univ ![1, -a] (by simp [Fin.sum_univ_succ]) 0 (by simp)
 #align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmpty
 
@@ -249,7 +249,7 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.Orientation ∨ x = -e.Orientation :=
   by
   induction' x using Module.Ray.ind with x hx
-  rw [← x.map_basis_ne_zero_iff e] at hx
+  rw [← x.map_basis_ne_zero_iff e] at hx 
   rwa [Basis.orientation, ray_eq_iff, neg_rayOfNeZero, ray_eq_iff, x.eq_smul_basis_det e,
     sameRay_neg_smul_left_iff_of_ne e.det_ne_zero hx, sameRay_smul_left_iff_of_ne e.det_ne_zero hx,
     lt_or_lt_iff_ne, ne_comm]

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

@@ -42,7 +42,7 @@ that index type is a `fintype` and there exists a basis of the same cardinality.
 
 noncomputable section
 
-open BigOperators
+open scoped BigOperators
 
 section OrderedCommSemiring
 

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

@@ -80,9 +80,6 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 #align orientation.map Orientation.map
 -/
 
-/- warning: orientation.map_apply -> Orientation.map_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
     Orientation.map ι e (rayOfNeZero _ v hv) =
@@ -90,23 +87,11 @@ theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι)
   rfl
 #align orientation.map_apply Orientation.map_apply
 
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 @[simp]
 theorem Orientation.map_refl : (Orientation.map ι <| LinearEquiv.refl R M) = Equiv.refl _ := by
   rw [Orientation.map, AlternatingMap.domLCongr_refl, Module.Ray.map_refl]
 #align orientation.map_refl Orientation.map_refl
 
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 @[simp]
 theorem Orientation.map_symm (e : M ≃ₗ[R] N) :
     (Orientation.map ι e).symm = Orientation.map ι e.symm :=
@@ -122,24 +107,12 @@ instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module
 #align is_empty.oriented IsEmpty.oriented
 -/
 
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 @[simp]
 theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty ι] (f : M ≃ₗ[R] N) :
     Orientation.map ι f positiveOrientation = positiveOrientation :=
   rfl
 #align orientation.map_positive_orientation_of_is_empty Orientation.map_positiveOrientation_of_isEmpty
 
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 @[simp]
 theorem Orientation.map_of_isEmpty [IsEmpty ι] (x : Orientation R M ι) (f : M ≃ₗ[R] M) :
     Orientation.map ι f x = x :=
@@ -160,9 +133,6 @@ variable {R : Type _} [StrictOrderedCommRing R]
 
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
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 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
     Orientation.map ι f (-x) = -Orientation.map ι f x :=
@@ -173,9 +143,6 @@ namespace Basis
 
 variable {ι : Type _}
 
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 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
 theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orientation R M ι)
@@ -199,20 +166,11 @@ protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι
 #align basis.orientation Basis.orientation
 -/
 
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 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).Orientation = Orientation.map ι f e.Orientation := by
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
 #align basis.orientation_map Basis.orientation_map
 
-/- warning: basis.orientation_units_smul -> Basis.orientation_unitsSMul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_units_smul Basis.orientation_unitsSMulₓ'. -/
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
 theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
@@ -224,12 +182,6 @@ theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
   simp
 #align basis.orientation_units_smul Basis.orientation_unitsSMul
 
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 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
 @[simp]
 theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
@@ -254,9 +206,6 @@ variable {ι : Type _}
 
 namespace Orientation
 
-/- warning: orientation.eq_or_eq_neg_of_is_empty -> Orientation.eq_or_eq_neg_of_isEmpty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmptyₓ'. -/
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
 mathematical sense if `M` is zero-dimensional.) -/
@@ -284,9 +233,6 @@ namespace Basis
 
 variable [Fintype ι] [DecidableEq ι]
 
-/- warning: basis.orientation_eq_iff_det_pos -> Basis.orientation_eq_iff_det_pos is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_posₓ'. -/
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
 theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
@@ -298,9 +244,6 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
     
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
 
-/- warning: basis.orientation_eq_or_eq_neg -> Basis.orientation_eq_or_eq_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_negₓ'. -/
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/
 theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.Orientation ∨ x = -e.Orientation :=
@@ -312,9 +255,6 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     lt_or_lt_iff_ne, ne_comm]
 #align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_neg
 
-/- warning: basis.orientation_ne_iff_eq_neg -> Basis.orientation_ne_iff_eq_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_negₓ'. -/
 /-- Given a basis, an orientation equals the negation of that given by that basis if and only
 if it does not equal that given by that basis. -/
 theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
@@ -323,9 +263,6 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     h.symm ▸ (Module.Ray.ne_neg_self e.Orientation).symm⟩
 #align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_neg
 
-/- warning: basis.orientation_comp_linear_equiv_eq_iff_det_pos -> Basis.orientation_comp_linearEquiv_eq_iff_det_pos is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
 theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -334,9 +271,6 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_pos
 
-/- warning: basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg -> Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg is a dubious translation:
-<too large>
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 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
 theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -345,9 +279,6 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg
 
-/- warning: basis.orientation_neg_single -> Basis.orientation_neg_single is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.orientation_neg_single Basis.orientation_neg_singleₓ'. -/
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
 @[simp]
@@ -368,12 +299,6 @@ def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Ori
 #align basis.adjust_to_orientation Basis.adjustToOrientation
 -/
 
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 /-- `adjust_to_orientation` gives a basis with the required orientation. -/
 @[simp]
 theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -386,9 +311,6 @@ theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis
     exact h
 #align basis.orientation_adjust_to_orientation Basis.orientation_adjustToOrientation
 
-/- warning: basis.adjust_to_orientation_apply_eq_or_eq_neg -> Basis.adjustToOrientation_apply_eq_or_eq_neg is a dubious translation:
-<too large>
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 /-- Every basis vector from `adjust_to_orientation` is either that from the original basis or its
 negation. -/
 theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -401,9 +323,6 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
   · by_cases hi : i = Classical.arbitrary ι <;> simp [units_smul_apply, hi]
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
 
-/- warning: basis.det_adjust_to_orientation -> Basis.det_adjustToOrientation is a dubious translation:
-<too large>
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 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
     (e.adjustToOrientation x).det = e.det ∨ (e.adjustToOrientation x).det = -e.det :=
@@ -416,9 +335,6 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     simp [e.det_units_smul, ← Units.coe_prod, Finset.prod_update_of_mem]
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
 
-/- warning: basis.abs_det_adjust_to_orientation -> Basis.abs_det_adjustToOrientation is a dubious translation:
-<too large>
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 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (v : ι → M) : |(e.adjustToOrientation x).det v| = |e.det v| := by
@@ -445,9 +361,6 @@ open FiniteDimensional
 
 include _i
 
-/- warning: orientation.eq_or_eq_neg -> Orientation.eq_or_eq_neg is a dubious translation:
-<too large>
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 /-- If the index type has cardinality equal to the finite dimension, any two orientations are
 equal or negations. -/
 theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -460,9 +373,6 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
     simp [h₁, h₂]
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg
 
-/- warning: orientation.ne_iff_eq_neg -> Orientation.ne_iff_eq_neg is a dubious translation:
-<too large>
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 /-- If the index type has cardinality equal to the finite dimension, an orientation equals the
 negation of another orientation if and only if they are not equal. -/
 theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -471,9 +381,6 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
     he.symm ▸ (Module.Ray.ne_neg_self x₂).symm⟩
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
 
-/- warning: orientation.map_eq_det_inv_smul -> Orientation.map_eq_det_inv_smul is a dubious translation:
-<too large>
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 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
 theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
@@ -484,9 +391,6 @@ theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 
 omit _i
 
-/- warning: orientation.map_eq_iff_det_pos -> Orientation.map_eq_iff_det_pos is a dubious translation:
-<too large>
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 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
 determinant is positive. -/
@@ -506,9 +410,6 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_self_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
 
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-<too large>
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 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and
 only if the determinant is negative. -/
@@ -539,12 +440,6 @@ def someBasis [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
 #align orientation.some_basis Orientation.someBasis
 -/
 
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 /-- `some_basis` gives a basis with the required orientation. -/
 @[simp]
 theorem someBasis_orientation [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)

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

@@ -81,10 +81,7 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 -/
 
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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) e))) hv))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.map_apply Orientation.map_applyₓ'. -/
 @[simp]
 theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
@@ -164,10 +161,7 @@ variable {R : Type _} [StrictOrderedCommRing R]
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
 /- warning: orientation.map_neg -> Orientation.map_neg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.map_neg Orientation.map_negₓ'. -/
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
@@ -180,10 +174,7 @@ namespace Basis
 variable {ι : Type _}
 
 /- warning: basis.map_orientation_eq_det_inv_smul -> Basis.map_orientation_eq_det_inv_smul is a dubious translation:
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toSemiring.{u1} R 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(StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AlternatingMap.zero.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} 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(StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MulOneClass.toMul.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (MulOneClass.toMul.{u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -220,10 +211,7 @@ theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
 #align basis.orientation_map Basis.orientation_map
 
 /- warning: basis.orientation_units_smul -> Basis.orientation_unitsSMul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u1} R] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Basis.orientation.{u1, u2, u3} R _inst_1 M _inst_2 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R 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(StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u3, u3} R R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u1) u2} R R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (SMulZeroClass.toSMul.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))))) (AlternatingMap.smul.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R 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_inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R 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(StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Finset.prod.{u3, u2} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) ι (CommGroup.toCommMonoid.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instCommGroupUnitsToMonoid.{u3} R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => w i))) (Basis.orientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_units_smul Basis.orientation_unitsSMulₓ'. -/
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
@@ -267,10 +255,7 @@ variable {ι : Type _}
 namespace Orientation
 
 /- warning: orientation.eq_or_eq_neg_of_is_empty -> Orientation.eq_or_eq_neg_of_isEmpty is a dubious translation:
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(LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Module.Oriented.positiveOrientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι (IsEmpty.oriented.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι _inst_4 _inst_5))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmptyₓ'. -/
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
@@ -300,10 +285,7 @@ namespace Basis
 variable [Fintype ι] [DecidableEq ι]
 
 /- warning: basis.orientation_eq_iff_det_pos -> Basis.orientation_eq_iff_det_pos is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_posₓ'. -/
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
@@ -317,10 +299,7 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
 
 /- warning: basis.orientation_eq_or_eq_neg -> Basis.orientation_eq_or_eq_neg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_negₓ'. -/
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/
 theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
@@ -334,10 +313,7 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
 #align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_neg
 
 /- warning: basis.orientation_ne_iff_eq_neg -> Basis.orientation_ne_iff_eq_neg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_negₓ'. -/
 /-- Given a basis, an orientation equals the negation of that given by that basis if and only
 if it does not equal that given by that basis. -/
@@ -348,10 +324,7 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
 #align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_neg
 
 /- warning: basis.orientation_comp_linear_equiv_eq_iff_det_pos -> Basis.orientation_comp_linearEquiv_eq_iff_det_pos is a dubious translation:
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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R 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-but is expected to have type
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_inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
@@ -362,10 +335,7 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
 #align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_pos
 
 /- warning: basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg -> Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg is a dubious translation:
-lean 3 declaration is
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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R 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_inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R 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-but is expected to have type
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_inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) 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_inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negₓ'. -/
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
@@ -376,10 +346,7 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
 #align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg
 
 /- warning: basis.orientation_neg_single -> Basis.orientation_neg_single is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.orientation_neg_single Basis.orientation_neg_singleₓ'. -/
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
@@ -420,10 +387,7 @@ theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis
 #align basis.orientation_adjust_to_orientation Basis.orientation_adjustToOrientation
 
 /- warning: basis.adjust_to_orientation_apply_eq_or_eq_neg -> Basis.adjustToOrientation_apply_eq_or_eq_neg is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_negₓ'. -/
 /-- Every basis vector from `adjust_to_orientation` is either that from the original basis or its
 negation. -/
@@ -438,10 +402,7 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
 
 /- warning: basis.det_adjust_to_orientation -> Basis.det_adjustToOrientation is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align basis.det_adjust_to_orientation Basis.det_adjustToOrientationₓ'. -/
 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
@@ -456,10 +417,7 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
 
 /- warning: basis.abs_det_adjust_to_orientation -> Basis.abs_det_adjustToOrientation is a dubious translation:
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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e) v))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.abs_det_adjust_to_orientation Basis.abs_det_adjustToOrientationₓ'. -/
 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -488,10 +446,7 @@ open FiniteDimensional
 include _i
 
 /- warning: orientation.eq_or_eq_neg -> Orientation.eq_or_eq_neg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.eq_or_eq_neg Orientation.eq_or_eq_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, any two orientations are
 equal or negations. -/
@@ -506,10 +461,7 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg
 
 /- warning: orientation.ne_iff_eq_neg -> Orientation.ne_iff_eq_neg is a dubious translation:
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_inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) x₂)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, an orientation equals the
 negation of another orientation if and only if they are not equal. -/
@@ -520,10 +472,7 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
 
 /- warning: orientation.map_eq_det_inv_smul -> Orientation.map_eq_det_inv_smul is a dubious translation:
-lean 3 declaration is
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(StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (Ring.toMonoid.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))))) (instMulActionRayToMonoidToDivInvMonoid.{u3, max (max u3 u2) u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MulOneClass.toMul.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M 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(RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
@@ -536,10 +485,7 @@ theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 omit _i
 
 /- warning: orientation.map_eq_iff_det_pos -> Orientation.map_eq_iff_det_pos is a dubious translation:
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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedRing.toStrictOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedCommRing.toLinearOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedField.toLinearOrderedCommRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) _inst_1)))))) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_posₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
@@ -561,10 +507,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
 
 /- warning: orientation.map_eq_neg_iff_det_neg -> Orientation.map_eq_neg_iff_det_neg is a dubious translation:
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(LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R 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R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) 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(LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R 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(DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommMonoidWithZero.toZero.{u3} ((fun 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R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommGroupWithZero.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedSemifield.toSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) _inst_1)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and

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

@@ -84,7 +84,7 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommSemiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_4] (ι : Type.{u4}) (e : LinearEquiv.{u1, u1, u2, u3} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) M N _inst_2 _inst_4 _inst_3 _inst_5) (v : AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (hv : Ne.{max (succ u2) (succ u1) (succ u4)} (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) v (OfNat.ofNat.{max u2 u1 u4} (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) 0 (OfNat.mk.{max u2 u1 u4} (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) 0 (Zero.zero.{max u2 u1 u4} (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (AlternatingMap.zero.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι))))), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) => (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) -> (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι e) (rayOfNeZero.{u1, max u2 u1 u4} R _inst_1 (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (AlternatingMap.module.{u1, u2, u1, u4, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Orientation._proof_1.{u1} R _inst_1)) v hv)) (rayOfNeZero.{u1, max u3 u1 u4} R _inst_1 (AlternatingMap.{u1, u3, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (AlternatingMap.addCommMonoid.{u1, u3, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι) (AlternatingMap.module.{u1, u3, u1, u4, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Orientation._proof_1.{u1} R _inst_1)) (AlternatingMap.compLinearMap.{u1, u2, u1, u4, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι N _inst_4 _inst_5 v ((fun (a : Sort.{max (succ u3) (succ u2)}) (b : Sort.{max (succ u3) (succ u2)}) [self : HasLiftT.{max (succ u3) (succ u2), max (succ u3) (succ u2)} a b] => self.0) (LinearEquiv.{u1, u1, u3, u2} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) 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_inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) ι N _inst_4 _inst_5 v (LinearEquiv.symm.{u1, u1, u2, u3} R R M N (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) e))) hv))
 but is expected to have type
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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.zero.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))), Eq.{max (max (succ u4) (succ u2)) (succ u1)} ((fun 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_inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) 0 (Zero.toOfNat0.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AddMonoid.toZero.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R 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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))))) (Eq.{max (max (succ u4) (succ u3)) (succ u1)} (AlternatingMap.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) v (OfNat.ofNat.{max 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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.compLinearMap.{u4, u3, u4, u1, u2} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι N _inst_4 _inst_5 v (LinearEquiv.toLinearMap.{u4, u4, u2, u3} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) N M _inst_4 _inst_2 _inst_5 _inst_3 (LinearEquiv.symm.{u4, u4, u3, u2} R R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) e))) (OfNat.ofNat.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) 0 (Zero.toOfNat0.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.zero.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))) (Eq.{max (max (succ u3) (succ u4)) (succ u1)} (AlternatingMap.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) v (OfNat.ofNat.{max (max u3 u4) u1} (AlternatingMap.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) 0 (Zero.toOfNat0.{max (max u3 u4) u1} (AlternatingMap.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.zero.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))) (AlternatingMap.compLinearEquiv_eq_zero_iff.{u2, u1, u4, u3, u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι N _inst_4 _inst_5 v (LinearEquiv.symm.{u4, u4, u3, u2} R R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) e))) hv))
 Case conversion may be inaccurate. Consider using '#align orientation.map_apply Orientation.map_applyₓ'. -/
 @[simp]
 theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
@@ -129,7 +129,7 @@ instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommSemiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_2] {N : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} N] [_inst_5 : Module.{u1, u3} R N (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_4] (ι : Type.{u4}) [_inst_6 : Nontrivial.{u1} R] [_inst_7 : IsEmpty.{succ u4} ι] (f : LinearEquiv.{u1, u1, u2, u3} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) M N _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) => (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) -> (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) (Module.Oriented.positiveOrientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι (IsEmpty.oriented.{u1, u2, u4} R _inst_1 M _inst_2 _inst_3 ι _inst_6 _inst_7))) (Module.Oriented.positiveOrientation.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι (IsEmpty.oriented.{u1, u3, u4} R _inst_1 N _inst_4 _inst_5 ι _inst_6 _inst_7))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommSemiring.{u4} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_2] {N : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} N] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_4] (ι : Type.{u3}) [_inst_6 : Nontrivial.{u4} R] [_inst_7 : IsEmpty.{succ u3} ι] (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) M N _inst_2 _inst_4 _inst_3 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι) (Module.Oriented.positiveOrientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι (IsEmpty.oriented.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_6 _inst_7))) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (fun (_x : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) (Module.Oriented.positiveOrientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι (IsEmpty.oriented.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_6 _inst_7))) (Module.Oriented.positiveOrientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι (IsEmpty.oriented.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι _inst_6 _inst_7))
+  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommSemiring.{u4} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_2] {N : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} N] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_4] (ι : Type.{u3}) [_inst_6 : Nontrivial.{u4} R] [_inst_7 : IsEmpty.{succ u3} ι] (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) M N _inst_2 _inst_4 _inst_3 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι) (Module.Oriented.positiveOrientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι (IsEmpty.oriented.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_6 _inst_7))) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (fun (_x : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R _inst_1 M _inst_2 _inst_3 N _inst_4 _inst_5 ι f) (Module.Oriented.positiveOrientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι (IsEmpty.oriented.{u4, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_6 _inst_7))) (Module.Oriented.positiveOrientation.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι (IsEmpty.oriented.{u4, u1, u3} R _inst_1 N _inst_4 _inst_5 ι _inst_6 _inst_7))
 Case conversion may be inaccurate. Consider using '#align orientation.map_positive_orientation_of_is_empty Orientation.map_positiveOrientation_of_isEmptyₓ'. -/
 @[simp]
 theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty ι] (f : M ≃ₗ[R] N) :
@@ -141,7 +141,7 @@ theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommSemiring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) _inst_2] (ι : Type.{u3}) [_inst_6 : IsEmpty.{succ u3} ι] (x : Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι)) => (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) -> (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Orientation.map.{u1, u2, u2, u3} R _inst_1 M _inst_2 _inst_3 M _inst_2 _inst_3 ι f) x) x
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : StrictOrderedCommSemiring.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) _inst_2] (ι : Type.{u3}) [_inst_6 : IsEmpty.{succ u3} ι] (x : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) x) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u1)) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (fun (_x : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Orientation.map.{u2, u1, u1, u3} R _inst_1 M _inst_2 _inst_3 M _inst_2 _inst_3 ι f) x) x
+  forall {R : Type.{u2}} [_inst_1 : StrictOrderedCommSemiring.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) _inst_2] (ι : Type.{u3}) [_inst_6 : IsEmpty.{succ u3} ι] (x : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) x) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u1)) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (fun (_x : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) => Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι) (Orientation.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι)) (Orientation.map.{u2, u1, u1, u3} R _inst_1 M _inst_2 _inst_3 M _inst_2 _inst_3 ι f) x) x
 Case conversion may be inaccurate. Consider using '#align orientation.map_of_is_empty Orientation.map_of_isEmptyₓ'. -/
 @[simp]
 theorem Orientation.map_of_isEmpty [IsEmpty ι] (x : Orientation R M ι) (f : M ≃ₗ[R] M) :
@@ -167,7 +167,7 @@ variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {ι : Type.{u4}} (f : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_5) (x : Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι) (coeFn.{max 1 (max 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 but is expected to have type
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(StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) x)) (Neg.neg.{max (max u3 u1) u4} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) x) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u1) u4} R _inst_1 (AlternatingMap.{u3, u1, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u3, u1, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u4, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u1)) (succ u4), max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Equiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u3, u2, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) x))
 Case conversion may be inaccurate. Consider using '#align orientation.map_neg Orientation.map_negₓ'. -/
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
@@ -183,7 +183,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (forall (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) => (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (Orientation.map.{u1, u2, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι f) x) (SMul.smul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (MulAction.toHasSmul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R 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R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det.{u1, u2} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1) M _inst_2 _inst_4) f)) x))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : StrictOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι], (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) -> (forall (x : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) => Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) x) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u1)) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M 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(CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M 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R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (MulAction.toSMul.{u2, max (max u2 u1) u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))))) (instMulActionRayToMonoidToDivInvMonoid.{u2, max (max u2 u1) u3, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AlternatingMap.zero.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instInv.{u2} R (MonoidWithZero.toMonoid.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (MulOneClass.toMul.{u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AlternatingMap.zero.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instInv.{u2} R (MonoidWithZero.toMonoid.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
 Case conversion may be inaccurate. Consider using '#align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -212,7 +212,7 @@ protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {ι : Type.{u4}} [_inst_6 : Fintype.{u4} ι] [_inst_7 : DecidableEq.{succ u4} ι] [_inst_8 : Nontrivial.{u1} R] (e : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_5), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι) (Basis.orientation.{u1, u3, u4} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u4, u1, u2, u3} ι R M N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 e f)) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) => (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι f) (Basis.orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommRing.{u4} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u4} R] (e : Basis.{u3, u4, u2} ι R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_4 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) (Basis.orientation.{u4, u1, u3} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u3, u4, u2, u1} ι R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 e f)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) (Basis.orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
+  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommRing.{u4} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u4} R] (e : Basis.{u3, u4, u2} ι R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_4 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) (Basis.orientation.{u4, u1, u3} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u3, u4, u2, u1} ι R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 e f)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) (Basis.orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_map Basis.orientation_mapₓ'. -/
 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).Orientation = Orientation.map ι f e.Orientation := by
@@ -351,7 +351,7 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) 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(CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R 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(CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
@@ -365,7 +365,7 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Neg.neg.{max (max u2 u1) u3} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u2, max (max u2 u1) u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u2} R (StrictOrderedRing.toOrderedAddCommGroup.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e))) (LT.lt.{u2} ((fun 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(StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} 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R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (StrictOrderedCommSemiring.toCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))) (LinearOrderedRing.isDomain.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedRing.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R 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(StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedRing.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negₓ'. -/
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
@@ -523,7 +523,7 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) => (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) -> (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} 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_inst_3 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R 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(StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R 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(Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (Ring.toMonoid.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R 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_inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) M _inst_2 _inst_3) f)) x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1), max (max (succ u3) (succ u2)) (succ u1)} (Equiv.{max (max (succ u1) (succ u2)) (succ u3), max (max (succ u1) (succ u2)) (succ u3)} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Orientation.{u3, u2, u1} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (MulAction.toSMul.{u3, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))))) (instMulActionRayToMonoidToDivInvMonoid.{u3, max (max u3 u2) u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MulOneClass.toMul.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι f) x) (HSMul.hSMul.{u3, max (max u3 u2) u1, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (instHSMul.{u3, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (MulAction.toSMul.{u3, max (max u3 u2) u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))))) (instMulActionRayToMonoidToDivInvMonoid.{u3, max (max u3 u2) u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R 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_inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MulOneClass.toMul.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} 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(Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
@@ -539,7 +539,7 @@ omit _i
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, 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(LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f))))
 but is expected to have type
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(DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (StrictOrderedRing.toPartialOrder.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedRing.toStrictOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedCommRing.toLinearOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedField.toLinearOrderedCommRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) _inst_1)))))) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) 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(LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, 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_inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [x : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (f : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 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R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (StrictOrderedRing.toPartialOrder.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedRing.toStrictOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedCommRing.toLinearOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedField.toLinearOrderedCommRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) _inst_1)))))) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_posₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
@@ -564,7 +564,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) => (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) -> (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Orientation.map.{u1, u2, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι f) x) (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) x)) (LT.lt.{u1} R (Preorder.toHasLt.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R 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(Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))))
 but is expected to have type
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(NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommMonoidWithZero.toZero.{u3} ((fun 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R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R 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R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) _inst_1)))))))))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) 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(DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommMonoidWithZero.toZero.{u3} ((fun 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 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and

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

@@ -301,7 +301,7 @@ variable [Fintype ι] [DecidableEq ι]
 
 /- warning: basis.orientation_eq_iff_det_pos -> Basis.orientation_eq_iff_det_pos is a dubious translation:
 lean 3 declaration is
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(LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) e₂)))
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (e₂ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e₁) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e₂)) (LT.lt.{u1} R (Preorder.toHasLt.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (coeFn.{max (succ u2) (succ u1) (succ u3), max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (fun (_x : AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) => (ι -> M) -> R) (AlternatingMap.coeFun.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e₁) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) e₂)))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (e₂ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₁) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₂)) (LT.lt.{u2} R (Preorder.toLT.{u2} R (PartialOrder.toPreorder.{u2} R (StrictOrderedRing.toPartialOrder.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))) (LinearOrderedRing.isDomain.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (AlternatingMap.{u2, u1, u2, u3} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u2, u1, u2, u3} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (Basis.det.{u2, u1, u3} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u3, succ u1} (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) e₂)))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_posₓ'. -/
@@ -349,7 +349,7 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
 
 /- warning: basis.orientation_comp_linear_equiv_eq_iff_det_pos -> Basis.orientation_comp_linearEquiv_eq_iff_det_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} 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u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)))
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e)) (LT.lt.{u1} R (Preorder.toHasLt.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (Preorder.toLT.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (StrictOrderedRing.toPartialOrder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R 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_inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
@@ -363,7 +363,7 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
 
 /- warning: basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg -> Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) 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(OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R 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(Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e))) (LT.lt.{u1} R (Preorder.toLT.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e))) (LT.lt.{u1} R (Preorder.toHasLt.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) 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(StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R 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(StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Neg.neg.{max (max u2 u1) u3} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u2, max (max u2 u1) u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u2} R (StrictOrderedRing.toOrderedAddCommGroup.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e))) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (Preorder.toLT.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) 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_inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negₓ'. -/
@@ -537,7 +537,7 @@ omit _i
 
 /- warning: orientation.map_eq_iff_det_pos -> Orientation.map_eq_iff_det_pos is a dubious translation:
 lean 3 declaration is
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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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(Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f))))
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, 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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f))))
 but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [x : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (f : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_posₓ'. -/
@@ -562,7 +562,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 
 /- warning: orientation.map_eq_neg_iff_det_neg -> Orientation.map_eq_neg_iff_det_neg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R 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(CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R 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(LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))))
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R 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(CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))))
 but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} 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(Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommGroupWithZero.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (Semifield.toCommGroupWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedSemifield.toSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_negₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.orientation
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
+! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Determinant
 /-!
 # Orientations of modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines orientations of modules.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -164,7 +164,7 @@ variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {ι : Type.{u4}} (f : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_5) (x : Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) => (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι f) (Neg.neg.{max u2 u1 u4} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u4} R _inst_1 (AlternatingMap.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u4, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) x)) (Neg.neg.{max u3 u1 u4} (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι) (Module.Ray.hasNeg.{u1, max u3 u1 u4} R _inst_1 (AlternatingMap.{u1, u3, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u1, u3, u1, u4} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u3, u1, u4, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) => (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι f) x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : StrictOrderedCommRing.{u3} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u3, u2} R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u3, u1} R N (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u4}} (f : LinearEquiv.{u3, u3, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (StrictOrderedRing.toRing.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_4 _inst_5) (x : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι), Eq.{max (max (succ u3) (succ u1)) (succ u4)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) (Neg.neg.{max (max u3 u2) u4} (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u2) u4} R _inst_1 (AlternatingMap.{u3, u2, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u3, u2, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u2, u3, u4, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u3, u2, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u2, u3, u4, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) x)) (Neg.neg.{max (max u3 u1) u4} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) x) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u1) u4} R _inst_1 (AlternatingMap.{u3, u1, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommGroup.{u3, u1, u3, u4} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u4, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u1)) (succ u4), max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Equiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u3, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u3, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u3, u2, u1, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) x))
 Case conversion may be inaccurate. Consider using '#align orientation.map_neg Orientation.map_negₓ'. -/
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
@@ -180,7 +180,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (forall (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) => (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι)) (Orientation.map.{u1, u2, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι f) x) (SMul.smul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (MulAction.toHasSmul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R 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_inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R 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_inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) => (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det.{u1, u2} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1) M _inst_2 _inst_4) f)) x))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : StrictOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι], (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) -> (forall (x : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (StrictOrderedCommRing.toStrictOrderedRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4), Eq.{max (max (succ u2) (succ u1)) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) => Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) x) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u1)) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι)) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) => Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u2) (succ u1)) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 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_inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (MulAction.toSMul.{u2, max (max u2 u1) u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))))) (instMulActionRayToMonoidToDivInvMonoid.{u2, max (max u2 u1) u3, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AlternatingMap.zero.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instInv.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (MulOneClass.toMul.{u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instGroupUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AlternatingMap.zero.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) f) (Units.instInv.{u2} R (MonoidWithZero.toMonoid.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) => Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
 Case conversion may be inaccurate. Consider using '#align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -209,7 +209,7 @@ protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} {N : Type.{u3}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} N] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3)] {ι : Type.{u4}} [_inst_6 : Fintype.{u4} ι] [_inst_7 : DecidableEq.{succ u4} ι] [_inst_8 : Nontrivial.{u1} R] (e : Basis.{u4, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_4 _inst_5), Eq.{succ (max u3 u1 u4)} (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι) (Basis.orientation.{u1, u3, u4} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u4, u1, u2, u3} ι R M N (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 e f)) (coeFn.{max 1 (max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))) (succ (max u3 u1 u4)) (succ (max u2 u1 u4)), max (succ (max u2 u1 u4)) (succ (max u3 u1 u4))} (Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (fun (_x : Equiv.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) => (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) -> (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u4), succ (max u3 u1 u4)} (Orientation.{u1, u2, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u1, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι)) (Orientation.map.{u1, u2, u3, u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u3} N _inst_3) _inst_5 ι f) (Basis.orientation.{u1, u2, u4} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
 but is expected to have type
-  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommRing.{u4} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u4} R] (e : Basis.{u3, u4, u2} ι R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (StrictOrderedRing.toRing.{u4} R (StrictOrderedCommRing.toStrictOrderedRing.{u4} R _inst_1))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_4 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) (Basis.orientation.{u4, u1, u3} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u3, u4, u2, u1} ι R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 e f)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) (Basis.orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
+  forall {R : Type.{u4}} [_inst_1 : StrictOrderedCommRing.{u4} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u4, u2} R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u4, u1} R N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u4} R] (e : Basis.{u3, u4, u2} ι R M (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (f : LinearEquiv.{u4, u4, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1)))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_4 _inst_5), Eq.{max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) (Basis.orientation.{u4, u1, u3} R _inst_1 N _inst_3 _inst_5 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.map.{u3, u4, u2, u1} ι R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 e f)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u1)) (succ u3), max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Equiv.{max (max (succ u3) (succ u2)) (succ u4), max (max (succ u3) (succ u1)) (succ u4)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (fun (_x : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) => Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι) _x) (Equiv.instFunLikeEquiv.{max (max (succ u4) (succ u2)) (succ u3), max (max (succ u4) (succ u1)) (succ u3)} (Orientation.{u4, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Orientation.{u4, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι)) (Orientation.map.{u4, u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u4} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) (Basis.orientation.{u4, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_map Basis.orientation_mapₓ'. -/
 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).Orientation = Orientation.map ι f e.Orientation := by
@@ -300,7 +300,7 @@ variable [Fintype ι] [DecidableEq ι]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (e₂ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e₁) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e₂)) (LT.lt.{u1} R (Preorder.toLT.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (coeFn.{max (succ u2) (succ u1) (succ u3), max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (fun (_x : AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) => (ι -> M) -> R) (AlternatingMap.coeFun.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e₁) (coeFn.{max (succ u3) (succ u1) (succ u2), max (succ u3) (succ u2)} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (fun (_x : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u2), succ u3, succ u2} (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) e₂)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (e₂ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₁) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₂)) (LT.lt.{u2} R (Preorder.toLT.{u2} R (PartialOrder.toPreorder.{u2} R (StrictOrderedRing.toPartialOrder.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))) (LinearOrderedRing.isDomain.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (AlternatingMap.{u2, u1, u2, u3} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u2, u1, u2, u3} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (Basis.det.{u2, u1, u3} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u3, succ u1} (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) e₂)))
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (e₂ : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₁) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e₂)) (LT.lt.{u2} R (Preorder.toLT.{u2} R (PartialOrder.toPreorder.{u2} R (StrictOrderedRing.toPartialOrder.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R (IsDomain.toCancelCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))) (LinearOrderedRing.isDomain.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} (AlternatingMap.{u2, u1, u2, u3} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u2, u1, u2, u3} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (Basis.det.{u2, u1, u3} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u3, succ u1} (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) e₂)))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_posₓ'. -/
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
@@ -348,7 +348,7 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e)) (LT.lt.{u1} R (Preorder.toLT.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R 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(CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
@@ -362,7 +362,7 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (Basis.map.{u3, u1, u2, u2} ι R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 e f)) (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (Infinite.nontrivial.{u1} R (CharZero.infinite.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))) (StrictOrderedSemiring.to_charZero.{u1} R (StrictOrderedRing.toStrictOrderedSemiring.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) e))) (LT.lt.{u1} R (Preorder.toLT.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Neg.neg.{max (max u2 u1) u3} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u2, max (max u2 u1) u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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(LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))) (LinearOrderedRing.isDomain.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedRing.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Neg.neg.{max (max u2 u1) u3} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u2, max (max u2 u1) u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u2} R (StrictOrderedRing.toOrderedAddCommGroup.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e))) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (Preorder.toLT.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))) (LinearOrderedRing.isDomain.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedCommRing.toLinearOrderedRing.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
 Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negₓ'. -/
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
@@ -438,7 +438,7 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : Nonempty.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), Or (Eq.{max (succ u2) (succ u1) (succ u3)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)) (Eq.{max (succ u2) (succ u1) (succ u3)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Neg.neg.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.neg.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Fintype.{u2} ι] [_inst_5 : DecidableEq.{succ u2} ι] [_inst_6 : Nontrivial.{u3} R] [_inst_7 : Nonempty.{succ u2} ι] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι), Or (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)) (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Neg.neg.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (AlternatingMap.neg.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Fintype.{u2} ι] [_inst_5 : DecidableEq.{succ u2} ι] [_inst_6 : Nontrivial.{u3} R] [_inst_7 : Nonempty.{succ u2} ι] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι), Or (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (AlternatingMap.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)) (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (AlternatingMap.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Neg.neg.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (AlternatingMap.neg.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)))
 Case conversion may be inaccurate. Consider using '#align basis.det_adjust_to_orientation Basis.det_adjustToOrientationₓ'. -/
 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
@@ -456,7 +456,7 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : Nonempty.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (v : ι -> M), Eq.{succ u1} R (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (LinearOrder.toLattice.{u1} R (LinearOrderedRing.toLinearOrder.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ u1) (succ u3), max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (fun (_x : AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) => (ι -> M) -> R) (AlternatingMap.coeFun.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) v)) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (LinearOrder.toLattice.{u1} R (LinearOrderedRing.toLinearOrder.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ u1) (succ u3), max (max (succ u3) (succ u2)) (succ u1)} (AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (fun (_x : AlternatingMap.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) => (ι -> M) -> R) (AlternatingMap.coeFun.{u1, u2, u1, u3} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (Basis.det.{u1, u2, u3} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e) v))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Fintype.{u2} ι] [_inst_5 : DecidableEq.{succ u2} ι] [_inst_6 : Nontrivial.{u3} R] [_inst_7 : Nonempty.{succ u2} ι] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (v : ι -> M), Eq.{succ u3} R (Abs.abs.{u3} R (Neg.toHasAbs.{u3} R (Ring.toNeg.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (SemilatticeSup.toSup.{u3} R (Lattice.toSemilatticeSup.{u3} R (DistribLattice.toLattice.{u3} R (instDistribLattice.{u3} R (LinearOrderedRing.toLinearOrder.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) v)) (Abs.abs.{u3} R (Neg.toHasAbs.{u3} R (Ring.toNeg.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (SemilatticeSup.toSup.{u3} R (Lattice.toSemilatticeSup.{u3} R (DistribLattice.toLattice.{u3} R (instDistribLattice.{u3} R (LinearOrderedRing.toLinearOrder.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e) v))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Fintype.{u2} ι] [_inst_5 : DecidableEq.{succ u2} ι] [_inst_6 : Nontrivial.{u3} R] [_inst_7 : Nonempty.{succ u2} ι] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (v : ι -> M), Eq.{succ u3} R (Abs.abs.{u3} R (Neg.toHasAbs.{u3} R (Ring.toNeg.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (SemilatticeSup.toSup.{u3} R (Lattice.toSemilatticeSup.{u3} R (DistribLattice.toLattice.{u3} R (instDistribLattice.{u3} R (LinearOrderedRing.toLinearOrder.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) v)) (Abs.abs.{u3} R (Neg.toHasAbs.{u3} R (Ring.toNeg.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (SemilatticeSup.toSup.{u3} R (Lattice.toSemilatticeSup.{u3} R (DistribLattice.toLattice.{u3} R (instDistribLattice.{u3} R (LinearOrderedRing.toLinearOrder.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u1) (succ u2), succ u3} (AlternatingMap.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (ι -> M) (fun (_x : ι -> M) => R) (AlternatingMap.funLike.{u3, u1, u3, u2} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e) v))
 Case conversion may be inaccurate. Consider using '#align basis.abs_det_adjust_to_orientation Basis.abs_det_adjustToOrientationₓ'. -/
 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -520,7 +520,7 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) => (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) -> (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Orientation.map.{u1, u2, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι f) x) (SMul.smul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (MulAction.toHasSmul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (Ring.toMonoid.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R 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(StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))))))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (fun (_x : MonoidHom.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) => (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) M _inst_2 _inst_3) f)) x))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R 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R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} 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_inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MulOneClass.toMul.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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_inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))))) (instMulActionRayToMonoidToDivInvMonoid.{u3, max (max u3 u2) u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R 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R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
@@ -536,7 +536,7 @@ omit _i
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (coeFn.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (fun (_x : Equiv.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R 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M _inst_2) _inst_3 ι)) (Equiv.hasCoeToFun.{succ (max u2 u1 u3), succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι)) (Orientation.map.{u1, u2, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι f) x) x) (LT.lt.{u1} R (Preorder.toLT.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R 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_inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [x : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (f : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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_inst_2) _inst_3 _inst_3 h)) (LinearOrderedCommRing.toLinearOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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_inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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_inst_2) _inst_3 _inst_3 h)) (CommGroupWithZero.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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_inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} 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_inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [x : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (f : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) (LinearOrderedRing.toStrictOrderedRing.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) _inst_1)))))) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h)) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R 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R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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_inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_posₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
@@ -561,7 +561,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R 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(NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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(MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R 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(Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) _inst_1)))))))))
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) => Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M 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(NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R 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(CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (CommMonoidWithZero.toZero.{u3} ((fun 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R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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_inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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 Case conversion may be inaccurate. Consider using '#align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -51,26 +51,38 @@ variable {N : Type _} [AddCommMonoid N] [Module R N]
 
 variable (ι : Type _)
 
+#print Orientation /-
 /-- An orientation of a module, intended to be used when `ι` is a `fintype` with the same
 cardinality as a basis. -/
 abbrev Orientation :=
   Module.Ray R (AlternatingMap R M R ι)
 #align orientation Orientation
+-/
 
+#print Module.Oriented /-
 /-- A type class fixing an orientation of a module. -/
 class Module.Oriented where
   positiveOrientation : Orientation R M ι
 #align module.oriented Module.Oriented
+-/
 
 export Module.Oriented (positiveOrientation)
 
 variable {R M}
 
+#print Orientation.map /-
 /-- An equivalence between modules implies an equivalence between orientations. -/
 def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N ι :=
   Module.Ray.map <| AlternatingMap.domLCongr R R ι R e
 #align orientation.map Orientation.map
+-/
 
+/- warning: orientation.map_apply -> Orientation.map_apply is a dubious translation:
+lean 3 declaration is
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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R _inst_1))) e))) hv))
+but is expected to have type
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(AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.compLinearMap.{u4, u3, u4, u1, u2} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι N _inst_4 _inst_5 v 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_inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) 0 (Zero.toOfNat0.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AddMonoid.toZero.{max (max u4 u1) u2} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R 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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))))) (Eq.{max (max (succ u4) (succ u3)) (succ u1)} (AlternatingMap.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) v (OfNat.ofNat.{max 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι) (AlternatingMap.zero.{u4, u3, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))) (Iff.mp (Eq.{max (max (succ u4) (succ u1)) (succ u2)} (AlternatingMap.{u4, u2, u4, u1} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) N _inst_4 _inst_5 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R 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(StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι)))) (AlternatingMap.compLinearEquiv_eq_zero_iff.{u2, u1, u4, u3, u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) M _inst_2 _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (Semiring.toModule.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) ι N _inst_4 _inst_5 v (LinearEquiv.symm.{u4, u4, u3, u2} R R M N (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (StrictOrderedSemiring.toSemiring.{u4} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u4} R _inst_1))) e))) hv))
+Case conversion may be inaccurate. Consider using '#align orientation.map_apply Orientation.map_applyₓ'. -/
 @[simp]
 theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
     Orientation.map ι e (rayOfNeZero _ v hv) =
@@ -78,30 +90,56 @@ theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι)
   rfl
 #align orientation.map_apply Orientation.map_apply
 
+/- warning: orientation.map_refl -> Orientation.map_refl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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 @[simp]
 theorem Orientation.map_refl : (Orientation.map ι <| LinearEquiv.refl R M) = Equiv.refl _ := by
   rw [Orientation.map, AlternatingMap.domLCongr_refl, Module.Ray.map_refl]
 #align orientation.map_refl Orientation.map_refl
 
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 @[simp]
 theorem Orientation.map_symm (e : M ≃ₗ[R] N) :
     (Orientation.map ι e).symm = Orientation.map ι e.symm :=
   rfl
 #align orientation.map_symm Orientation.map_symm
 
+#print IsEmpty.oriented /-
 /-- A module is canonically oriented with respect to an empty index type. -/
 instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι
     where positiveOrientation :=
     rayOfNeZero R (AlternatingMap.constLinearEquivOfIsEmpty 1) <|
       AlternatingMap.constLinearEquivOfIsEmpty.Injective.Ne (by simp)
 #align is_empty.oriented IsEmpty.oriented
+-/
 
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 @[simp]
 theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty ι] (f : M ≃ₗ[R] N) :
     Orientation.map ι f positiveOrientation = positiveOrientation :=
   rfl
 #align orientation.map_positive_orientation_of_is_empty Orientation.map_positiveOrientation_of_isEmpty
 
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+Case conversion may be inaccurate. Consider using '#align orientation.map_of_is_empty Orientation.map_of_isEmptyₓ'. -/
 @[simp]
 theorem Orientation.map_of_isEmpty [IsEmpty ι] (x : Orientation R M ι) (f : M ≃ₗ[R] M) :
     Orientation.map ι f x = x :=
@@ -122,6 +160,12 @@ variable {R : Type _} [StrictOrderedCommRing R]
 
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
+/- warning: orientation.map_neg -> Orientation.map_neg is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : StrictOrderedCommRing.{u3} R] {M : Type.{u2}} {N : Type.{u1}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u1} N] [_inst_4 : Module.{u3, u2} R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u3, u1} R N (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} N _inst_3)] {ι : Type.{u4}} (f : LinearEquiv.{u3, u3, u2, u1} R R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R 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_inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N (AddCommGroup.toAddCommMonoid.{u1} N _inst_3) _inst_5 ι f) x))
+Case conversion may be inaccurate. Consider using '#align orientation.map_neg Orientation.map_negₓ'. -/
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
     Orientation.map ι f (-x) = -Orientation.map ι f x :=
@@ -132,6 +176,12 @@ namespace Basis
 
 variable {ι : Type _}
 
+/- warning: basis.map_orientation_eq_det_inv_smul -> Basis.map_orientation_eq_det_inv_smul is a dubious translation:
+lean 3 declaration is
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(StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toSemiring.{u1} R 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_inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) => (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det._proof_1.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (LinearEquiv.det._proof_2.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))) (LinearEquiv.det.{u1, u2} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1) M _inst_2 _inst_4) f)) x))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : StrictOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_4 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Finite.{succ u3} ι], (Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) -> (forall (x : Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u2} R R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))))) (Units.smulCommClass_right.{u2, u2, max (max u2 u1) u3} R R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (SMulZeroClass.toSMul.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (SMulWithZero.toSMulZeroClass.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (StrictOrderedCommSemiring.toCommSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u2 u1) u3} (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (AlternatingMap.addCommMonoid.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))))) (AlternatingMap.smul.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u2} R R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (smulCommClass_self.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι) (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, max (max u2 u1) u3} R (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R _inst_1)))) (smulCommClass_self.{u2, u2} R R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)) (Monoid.toMulAction.{u2} R (CommMonoid.toMonoid.{u2} R (CommRing.toCommMonoid.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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(Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (MulOneClass.toMul.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (MulOneClass.toMul.{u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))) (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))))) (Monoid.toMulOneClass.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (DivInvMonoid.toMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R 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_inst_4 _inst_4) (Group.toDivInvMonoid.{u1} (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4) (LinearEquiv.automorphismGroup.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Units.instMulOneClassUnits.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1))))))))) (LinearEquiv.det.{u2, u1} R (StrictOrderedCommRing.toCommRing.{u2} R _inst_1) M _inst_2 _inst_4) f)) x))
+Case conversion may be inaccurate. Consider using '#align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
 theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orientation R M ι)
@@ -148,16 +198,30 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
 
 variable [Fintype ι] [DecidableEq ι]
 
+#print Basis.orientation /-
 /-- The orientation given by a basis. -/
 protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι :=
   rayOfNeZero R _ e.det_ne_zero
 #align basis.orientation Basis.orientation
+-/
 
+/- warning: basis.orientation_map -> Basis.orientation_map is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.orientation_map Basis.orientation_mapₓ'. -/
 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).Orientation = Orientation.map ι f e.Orientation := by
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
 #align basis.orientation_map Basis.orientation_map
 
+/- warning: basis.orientation_units_smul -> Basis.orientation_unitsSMul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u1} R] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Basis.orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.unitsSMul.{u3, u1, u2} ι R M (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)) _inst_2 _inst_4 e w)) (SMul.smul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (MulAction.toHasSmul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1)))) ι R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (smulCommClass_self.{u1, u1} R R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))))))))))) (Inv.inv.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Units.hasInv.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Finset.prod.{u1, u3} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) ι (CommGroup.toCommMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1)))) (Units.instCommGroupUnitsToMonoid.{u1} R (CommRing.toCommMonoid.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R _inst_1)))) (Finset.univ.{u3} ι _inst_6) (fun (i : ι) => w i))) (Basis.orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : StrictOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_4 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u2} ι] [_inst_8 : Nontrivial.{u3} R] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (w : ι -> (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))))), Eq.{max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (Basis.orientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 (Basis.unitsSMul.{u2, u3, u1} ι R M (StrictOrderedRing.toRing.{u3} R (StrictOrderedCommRing.toStrictOrderedRing.{u3} R _inst_1)) _inst_2 _inst_4 e w)) (HSMul.hSMul.{u3, max (max u3 u1) u2, max (max u3 u1) u2} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (instHSMul.{u3, max (max u3 u1) u2} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (MulAction.toSMul.{u3, max (max u3 u1) u2} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (DivInvMonoid.toMonoid.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Group.toDivInvMonoid.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))))) (instMulActionRayToMonoidToDivInvMonoid.{u3, max (max u3 u1) u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R 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(StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι)) (AlternatingMap.distribMulAction.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u3, u3} R R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R 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(StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R 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(StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u2} (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))))) (AlternatingMap.smul.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u3, u3} R R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (AlternatingMap.zero.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u1) u2} R (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AlternatingMap.addCommMonoid.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))) (smulCommClass_self.{u3, u3} R R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Finset.prod.{u3, u2} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) ι (CommGroup.toCommMonoid.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1)))))) (Units.instCommGroupUnitsToMonoid.{u3} R (CommRing.toCommMonoid.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R _inst_1)))) (Finset.univ.{u2} ι _inst_6) (fun (i : ι) => w i))) (Basis.orientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 e))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_units_smul Basis.orientation_unitsSMulₓ'. -/
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
 theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
@@ -169,6 +233,12 @@ theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
   simp
 #align basis.orientation_units_smul Basis.orientation_unitsSMul
 
+/- warning: basis.orientation_is_empty -> Basis.orientation_isEmpty is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] [_inst_7 : DecidableEq.{succ u3} ι] [_inst_8 : Nontrivial.{u1} R] [_inst_9 : IsEmpty.{succ u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (StrictOrderedCommRing.toStrictOrderedRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι) (Basis.orientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 b) (Module.Oriented.positiveOrientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι (IsEmpty.oriented.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 ι _inst_8 _inst_9))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : StrictOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_4 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u2} ι] [_inst_8 : Nontrivial.{u3} R] [_inst_9 : IsEmpty.{succ u2} ι] (b : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4), Eq.{max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι) (Basis.orientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_4 ι _inst_6 (fun (a : ι) (b : ι) => _inst_7 a b) _inst_8 b) (Module.Oriented.positiveOrientation.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι (IsEmpty.oriented.{u3, u1, u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 ι _inst_8 _inst_9))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_is_empty Basis.orientation_isEmptyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
 @[simp]
 theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
@@ -193,6 +263,12 @@ variable {ι : Type _}
 
 namespace Orientation
 
+/- warning: orientation.eq_or_eq_neg_of_is_empty -> Orientation.eq_or_eq_neg_of_isEmpty is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Nontrivial.{u1} R] [_inst_5 : IsEmpty.{succ u3} ι] (o : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), Or (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) o (Module.Oriented.positiveOrientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι (IsEmpty.oriented.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι _inst_4 _inst_5))) (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) o (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Module.Oriented.positiveOrientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι (IsEmpty.oriented.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι _inst_4 _inst_5))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Nontrivial.{u3} R] [_inst_5 : IsEmpty.{succ u2} ι] (o : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι), Or (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) o (Module.Oriented.positiveOrientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι (IsEmpty.oriented.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι _inst_4 _inst_5))) (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) o (Neg.neg.{max (max u2 u1) u3} (Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u1) u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1) (AlternatingMap.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u3, u1, u3, u2} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1))))) (Module.Oriented.positiveOrientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι (IsEmpty.oriented.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι _inst_4 _inst_5))))
+Case conversion may be inaccurate. Consider using '#align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmptyₓ'. -/
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
 mathematical sense if `M` is zero-dimensional.) -/
@@ -220,6 +296,12 @@ namespace Basis
 
 variable [Fintype ι] [DecidableEq ι]
 
+/- warning: basis.orientation_eq_iff_det_pos -> Basis.orientation_eq_iff_det_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e₁ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (e₂ : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) e₂)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_posₓ'. -/
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
 theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
@@ -231,6 +313,12 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
     
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
 
+/- warning: basis.orientation_eq_or_eq_neg -> Basis.orientation_eq_or_eq_neg is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u2, u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι), Or (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) x (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)) (Eq.{max (max (succ u2) (succ u1)) (succ 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R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e)))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_negₓ'. -/
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/
 theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.Orientation ∨ x = -e.Orientation :=
@@ -242,6 +330,12 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     lt_or_lt_iff_ne, ne_comm]
 #align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_neg
 
+/- warning: basis.orientation_ne_iff_eq_neg -> Basis.orientation_ne_iff_eq_neg is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_negₓ'. -/
 /-- Given a basis, an orientation equals the negation of that given by that basis if and only
 if it does not equal that given by that basis. -/
 theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
@@ -250,6 +344,12 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     h.symm ▸ (Module.Ray.ne_neg_self e.Orientation).symm⟩
 #align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_neg
 
+/- warning: basis.orientation_comp_linear_equiv_eq_iff_det_pos -> Basis.orientation_comp_linearEquiv_eq_iff_det_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) f)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_posₓ'. -/
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
 theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -258,6 +358,12 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_pos
 
+/- warning: basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg -> Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) => (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> R) (MonoidHom.hasCoeToFun.{u2, u1} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))))))) (LinearMap.det.{u2, u1} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R 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(LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedCommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f : LinearEquiv.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Iff (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (Basis.map.{u3, u2, u1, u1} ι R M M (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 e f)) (Neg.neg.{max (max u2 u1) u3} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u2, max (max u2 u1) u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) (AlternatingMap.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.addCommGroup.{u2, u1, u2, u3} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u2} R (StrictOrderedRing.toOrderedAddCommGroup.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι) (AlternatingMap.module.{u2, u1, u2, u3, u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Orientation.proof_1.{u2} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) (instNontrivial.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1))))) (StrictOrderedSemiring.to_charZero.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) e))) (LT.lt.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (Preorder.toLT.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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(LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedRing.toStrictOrderedRing.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) 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_inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1))))))) (MonoidHom.monoidHomClass.{u1, u2} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))))))) (LinearMap.det.{u1, u2} M _inst_2 R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)) _inst_3) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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(StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R (StrictOrderedCommRing.toCommRing.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u2, u2, u1, u1} R R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (StrictOrderedRing.toRing.{u2} R (LinearOrderedRing.toStrictOrderedRing.{u2} R (LinearOrderedCommRing.toLinearOrderedRing.{u2} R _inst_1)))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1)))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) (RingHomInvPair.ids.{u2} R (StrictOrderedSemiring.toSemiring.{u2} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 f)) _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negₓ'. -/
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
 theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -266,6 +372,12 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg
 
+/- warning: basis.orientation_neg_single -> Basis.orientation_neg_single is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] [_inst_6 : Nontrivial.{u1} R] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (i : ι), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))))) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 e))
+but is expected to have type
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(LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u3, u1, u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 (Basis.unitsSMul.{u2, u3, u1} ι R M (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))) _inst_2 _inst_3 e (Function.update.{succ u2, succ u3} ι (fun (ᾰ : ι) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u3 u2} (ι -> (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))))))) 1 (One.toOfNat1.{max u3 u2} (ι -> (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1)))))))) (Pi.instOne.{u2, u3} ι (fun (a : ι) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) (fun (i : ι) => InvOneClass.toOne.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (StrictOrderedRing.toRing.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R _inst_1))))))) 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(StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (AlternatingMap.module.{u3, u1, u3, u2, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) (Orientation.proof_1.{u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) (Basis.orientation.{u3, u1, u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 e))
+Case conversion may be inaccurate. Consider using '#align basis.orientation_neg_single Basis.orientation_neg_singleₓ'. -/
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
 @[simp]
@@ -276,6 +388,7 @@ theorem orientation_neg_single [Nontrivial R] (e : Basis ι R M) (i : ι) :
   simp
 #align basis.orientation_neg_single Basis.orientation_neg_single
 
+#print Basis.adjustToOrientation /-
 /-- Given a basis and an orientation, return a basis giving that orientation: either the original
 basis, or one constructed by negating a single (arbitrary) basis vector. -/
 def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Orientation R M ι) :
@@ -283,7 +396,14 @@ def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Ori
   haveI := Classical.decEq (Orientation R M ι)
   if e.orientation = x then e else e.units_smul (Function.update 1 (Classical.arbitrary ι) (-1))
 #align basis.adjust_to_orientation Basis.adjustToOrientation
+-/
 
+/- warning: basis.orientation_adjust_to_orientation -> Basis.orientation_adjustToOrientation is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_inst_5 : DecidableEq.{succ u3} ι] [_inst_6 : Nontrivial.{u1} R] [_inst_7 : Nonempty.{succ u3} ι] (e : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1)) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 (Basis.adjustToOrientation.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) x
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.orientation_adjust_to_orientation Basis.orientation_adjustToOrientationₓ'. -/
 /-- `adjust_to_orientation` gives a basis with the required orientation. -/
 @[simp]
 theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -296,6 +416,12 @@ theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis
     exact h
 #align basis.orientation_adjust_to_orientation Basis.orientation_adjustToOrientation
 
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+Case conversion may be inaccurate. Consider using '#align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_negₓ'. -/
 /-- Every basis vector from `adjust_to_orientation` is either that from the original basis or its
 negation. -/
 theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
@@ -308,6 +434,12 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
   · by_cases hi : i = Classical.arbitrary ι <;> simp [units_smul_apply, hi]
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
 
+/- warning: basis.det_adjust_to_orientation -> Basis.det_adjustToOrientation is a dubious translation:
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+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedCommRing.{u3} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u3, u1} R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u2}} [_inst_4 : Fintype.{u2} ι] [_inst_5 : DecidableEq.{succ u2} ι] [_inst_6 : Nontrivial.{u3} R] [_inst_7 : Nonempty.{succ u2} ι] (e : Basis.{u2, u3, u1} ι R M (StrictOrderedSemiring.toSemiring.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (x : Orientation.{u3, u1, u2} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R 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(LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 (Basis.adjustToOrientation.{u3, u1, u2} R _inst_1 M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_7 e x)) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)) (Eq.{max (max (succ u3) (succ u1)) (succ u2)} (AlternatingMap.{u3, u1, u3, u2} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R 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(StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e)))
+Case conversion may be inaccurate. Consider using '#align basis.det_adjust_to_orientation Basis.det_adjustToOrientationₓ'. -/
 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
     (e.adjustToOrientation x).det = e.det ∨ (e.adjustToOrientation x).det = -e.det :=
@@ -320,6 +452,12 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     simp [e.det_units_smul, ← Units.coe_prod, Finset.prod_update_of_mem]
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
 
+/- warning: basis.abs_det_adjust_to_orientation -> Basis.abs_det_adjustToOrientation is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1))))) ι) (Basis.det.{u3, u1, u2} R (StrictOrderedCommRing.toCommRing.{u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R _inst_1)) M _inst_2 _inst_3 ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_4 e) v))
+Case conversion may be inaccurate. Consider using '#align basis.abs_det_adjust_to_orientation Basis.abs_det_adjustToOrientationₓ'. -/
 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (v : ι → M) : |(e.adjustToOrientation x).det v| = |e.det v| := by
@@ -346,6 +484,12 @@ open FiniteDimensional
 
 include _i
 
+/- warning: orientation.eq_or_eq_neg -> Orientation.eq_or_eq_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] (x₁ : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (x₂ : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Or (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ x₂) (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) x₂)))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x₁ : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (x₂ : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Or (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ x₂) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ (Neg.neg.{max (max u3 u2) u1} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u2) u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) x₂)))
+Case conversion may be inaccurate. Consider using '#align orientation.eq_or_eq_neg Orientation.eq_or_eq_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, any two orientations are
 equal or negations. -/
 theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -358,6 +502,12 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
     simp [h₁, h₂]
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg
 
+/- warning: orientation.ne_iff_eq_neg -> Orientation.ne_iff_eq_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] (x₁ : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (x₂ : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Ne.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ x₂) (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ (Neg.neg.{max u2 u1 u3} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Module.Ray.hasNeg.{u1, max u2 u1 u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) x₂)))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x₁ : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (x₂ : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι), (Eq.{1} Nat (Fintype.card.{u1} ι _inst_4) (FiniteDimensional.finrank.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Ne.{max (max (succ u3) (succ u2)) (succ u1)} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ x₂) (Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) x₁ (Neg.neg.{max (max u3 u2) u1} (Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (instNegRayToStrictOrderedCommSemiringToAddCommMonoid.{u3, max (max u3 u2) u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommGroup.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedAddCommGroup.toAddCommGroup.{u3} R (StrictOrderedRing.toOrderedAddCommGroup.{u3} R (LinearOrderedRing.toStrictOrderedRing.{u3} R (LinearOrderedCommRing.toLinearOrderedRing.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) x₂)))
+Case conversion may be inaccurate. Consider using '#align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, an orientation equals the
 negation of another orientation if and only if they are not equal. -/
 theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -366,6 +516,12 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
     he.symm ▸ (Module.Ray.ne_neg_self x₂).symm⟩
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
 
+/- warning: orientation.map_eq_det_inv_smul -> Orientation.map_eq_det_inv_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι f) x) (SMul.smul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (MulAction.toHasSmul.{u1, max u2 u1 u3} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Module.Ray.mulAction.{u1, max u2 u1 u3, u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (AlternatingMap.distribMulAction.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (DivInvMonoid.toMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Group.toDivInvMonoid.{u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Units.group.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))) (Units.distribMulAction.{u1, u1} R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, u1} R R R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, u1} R R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (Module.toMulActionWithZero.{u1, u1} R R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))))))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))) (Units.smulCommClass_right.{u1, u1, max u2 u1 u3} R R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (SMulZeroClass.toHasSmul.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddMonoid.toAddZeroClass.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι)))) (Module.toMulActionWithZero.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (AlternatingMap.addCommMonoid.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AlternatingMap.module.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Orientation._proof_1.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))))))) (AlternatingMap.smul.{u1, u2, u1, u3, u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι R (Ring.toMonoid.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (StrictOrderedRing.toOrderedAddCommGroup.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (smulCommClass_self.{u1, u1} R R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (Monoid.toMulAction.{u1} R (CommMonoid.toMonoid.{u1} R (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (smulCommClass_self.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, max u2 u1 u3} R (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) 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(LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max u2 u1 u3} (AlternatingMap.{u1, u2, u1, u3} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u1} R 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(Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R 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_inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) -> (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (MonoidHom.hasCoeToFun.{u2, u1} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det._proof_1.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (LinearEquiv.det._proof_2.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.mulOneClass.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) (LinearEquiv.det.{u1, u2} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) M _inst_2 _inst_3) f)) x))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [_i : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (x : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instGroupUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instDistribMulActionUnitsToMonoidToDivInvMonoidInstGroupUnits.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι)) (AlternatingMap.distribMulAction.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (Module.toDistribMulAction.{u3, u3} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))))))) (Units.smulCommClass_right.{u3, u3, max (max u3 u2) u1} R R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (SMulWithZero.toSMulZeroClass.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (StrictOrderedCommSemiring.toCommSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (MulActionWithZero.toSMulWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (AddMonoid.toZero.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AddCommMonoid.toAddMonoid.{max (max u3 u2) u1} (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι))) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Orientation.proof_1.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))))))) (AlternatingMap.smul.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)))))) (smulCommClass_self.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (AlternatingMap.zero.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (Module.toMulActionWithZero.{u3, max (max u3 u2) u1} R (AlternatingMap.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AlternatingMap.addCommMonoid.{u3, u2, u3, u1} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι) (AlternatingMap.module.{u3, u2, u3, u1, u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 R (OrderedCancelAddCommMonoid.toAddCommMonoid.{u3} R (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (Semiring.toModule.{u3} R (StrictOrderedSemiring.toSemiring.{u3} R (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) ι R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (smulCommClass_self.{u3, u3} R R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1)) (Monoid.toMulAction.{u3} R (CommMonoid.toMonoid.{u3} R (LinearOrderedCommRing.toCommMonoid.{u3} R (LinearOrderedField.toLinearOrderedCommRing.{u3} R _inst_1))))))))))))) (Inv.inv.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) f) (Units.instInv.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} 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_inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MulOneClass.toMul.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) (MulOneClass.toMul.{u3} (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R 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(DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Units.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (Monoid.toMulOneClass.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (DivInvMonoid.toMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Group.toDivInvMonoid.{u2} (LinearEquiv.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.automorphismGroup.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (Units.instMulOneClassUnits.{u3} R (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearEquiv.det.{u3, u2} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) M _inst_2 _inst_3) f)) x))
+Case conversion may be inaccurate. Consider using '#align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smulₓ'. -/
 /-- The value of `orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
 theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
@@ -376,6 +532,12 @@ theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 
 omit _i
 
+/- warning: orientation.map_eq_iff_det_pos -> Orientation.map_eq_iff_det_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, 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(EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) (LinearMap.det.{u2, u1} M _inst_2 R (EuclideanDomain.toCommRing.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R 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_inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : LinearOrderedField.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u1}} [_inst_4 : Fintype.{u1} ι] [x : FiniteDimensional.{u3, u2} R M (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)) _inst_2 _inst_3] (f : Orientation.{u3, u2, u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : LinearEquiv.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (a : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) a) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} 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(NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) 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(EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))))) (LinearMap.det.{u2, u3} M _inst_2 R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))) _inst_3) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 h))))
+Case conversion may be inaccurate. Consider using '#align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_posₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
 determinant is positive. -/
@@ -395,6 +557,12 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_self_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
 
+/- warning: orientation.map_eq_neg_iff_det_neg -> Orientation.map_eq_neg_iff_det_neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)) -> (Iff (Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, 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R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R 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(Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) 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(DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))))))))) f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))))))))))))
+but is expected to have type
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(MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulOneClass.toMul.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3)))))) (MulOneClass.toMul.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))))) (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u3} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) R (MulZeroOneClass.toMulOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocSemiring.toMulZeroOneClass.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (NonAssocRing.toNonAssocSemiring.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Ring.toNonAssocRing.{u2} (LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.ring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) _inst_2 _inst_3))))) (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) (LinearOrderedField.toLinearOrderedSemifield.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (LinearOrderedField.toField.{u3} R _inst_1))))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => R) (LinearEquiv.toLinearMap.{u3, u3, u2, u2} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (DivisionRing.toRing.{u3} R (Field.toDivisionRing.{u3} R (LinearOrderedField.toField.{u3} R _inst_1)))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1)))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) (RingHomInvPair.ids.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (LinearOrderedSemifield.toSemifield.{u3} R (LinearOrderedField.toLinearOrderedSemifield.{u3} R _inst_1))))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 f)) _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_negₓ'. -/
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and
 only if the determinant is negative. -/
@@ -416,13 +584,21 @@ theorem map_eq_neg_iff_det_neg (x : Orientation R M ι) (f : M ≃ₗ[R] M)
 
 include _i
 
+#print Orientation.someBasis /-
 /-- If the index type has cardinality equal to the finite dimension, a basis with the given
 orientation. -/
 def someBasis [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
     (h : Fintype.card ι = finrank R M) : Basis ι R M :=
   ((finBasis R M).reindex (Fintype.equivFinOfCardEq h).symm).adjustToOrientation x
 #align orientation.some_basis Orientation.someBasis
+-/
 
+/- warning: orientation.some_basis_orientation -> Orientation.someBasis_orientation is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u1, u2} R M (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)) _inst_2 _inst_3] [_inst_5 : Nonempty.{succ u3} ι] [_inst_6 : DecidableEq.{succ u3} ι] (x : Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (h : Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u1, u2} R M (Ring.toSemiring.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R (LinearOrderedField.toField.{u1} R _inst_1)))) _inst_2 _inst_3)), Eq.{succ (max u2 u1 u3)} (Orientation.{u1, u2, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 ι) (Basis.orientation.{u1, u2, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R (LinearOrderedField.toLinearOrderedCommRing.{u1} R _inst_1)) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_6 a b) (EuclideanDomain.to_nontrivial.{u1} R (Field.toEuclideanDomain.{u1} R (LinearOrderedField.toField.{u1} R _inst_1))) (Orientation.someBasis.{u1, u2, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 _i _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) x h)) x
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (LinearOrderedSemifield.toSemifield.{u2} R (LinearOrderedField.toLinearOrderedSemifield.{u2} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {ι : Type.{u3}} [_inst_4 : Fintype.{u3} ι] [_i : FiniteDimensional.{u2, u1} R M (Field.toDivisionRing.{u2} R (LinearOrderedField.toField.{u2} R _inst_1)) _inst_2 _inst_3] [_inst_5 : Nonempty.{succ u3} ι] [_inst_6 : DecidableEq.{succ u3} ι] (x : Orientation.{u2, u1, u3} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} R (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} R (LinearOrderedField.toLinearOrderedSemifield.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (h : Eq.{1} Nat (Fintype.card.{u3} ι _inst_4) (FiniteDimensional.finrank.{u2, u1} R M (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (LinearOrderedSemifield.toSemifield.{u2} R (LinearOrderedField.toLinearOrderedSemifield.{u2} R _inst_1)))) _inst_2 _inst_3)), Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Orientation.{u2, u1, u3} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R (LinearOrderedField.toLinearOrderedCommRing.{u2} R _inst_1))) M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 ι) (Basis.orientation.{u2, u1, u3} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u2} R (LinearOrderedField.toLinearOrderedCommRing.{u2} R _inst_1)) M _inst_2 _inst_3 ι _inst_4 (fun (a : ι) (b : ι) => _inst_6 a b) (EuclideanDomain.toNontrivial.{u2} R (Field.toEuclideanDomain.{u2} R (LinearOrderedField.toField.{u2} R _inst_1))) (Orientation.someBasis.{u2, u1, u3} R _inst_1 M _inst_2 _inst_3 ι _inst_4 _i _inst_5 (fun (a : ι) (b : ι) => _inst_6 a b) x h)) x
+Case conversion may be inaccurate. Consider using '#align orientation.some_basis_orientation Orientation.someBasis_orientationₓ'. -/
 /-- `some_basis` gives a basis with the required orientation. -/
 @[simp]
 theorem someBasis_orientation [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -160,14 +160,14 @@ theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
 
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
-theorem orientation_unitsSmul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
+theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
     (e.units_smul w).Orientation = (∏ i, w i)⁻¹ • e.Orientation :=
   by
   rw [Basis.orientation, Basis.orientation, smul_rayOfNeZero, ray_eq_iff,
     e.det.eq_smul_basis_det (e.units_smul w), det_units_smul_self, Units.smul_def, smul_smul]
   norm_cast
   simp
-#align basis.orientation_units_smul Basis.orientation_unitsSmul
+#align basis.orientation_units_smul Basis.orientation_unitsSMul
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -68,7 +68,7 @@ variable {R M}
 
 /-- An equivalence between modules implies an equivalence between orientations. -/
 def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N ι :=
-  Module.Ray.map <| AlternatingMap.domLcongr R R ι R e
+  Module.Ray.map <| AlternatingMap.domLCongr R R ι R e
 #align orientation.map Orientation.map
 
 @[simp]
@@ -80,7 +80,7 @@ theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι)
 
 @[simp]
 theorem Orientation.map_refl : (Orientation.map ι <| LinearEquiv.refl R M) = Equiv.refl _ := by
-  rw [Orientation.map, AlternatingMap.domLcongr_refl, Module.Ray.map_refl]
+  rw [Orientation.map, AlternatingMap.domLCongr_refl, Module.Ray.map_refl]
 #align orientation.map_refl Orientation.map_refl
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.orientation
-! leanprover-community/mathlib commit bdcb5fb7877d5f341028f489c3337526832c95a8
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -49,7 +49,7 @@ variable (M : Type _) [AddCommMonoid M] [Module R M]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
-variable (ι : Type _) [DecidableEq ι]
+variable (ι : Type _)
 
 /-- An orientation of a module, intended to be used when `ι` is a `fintype` with the same
 cardinality as a basis. -/
@@ -123,14 +123,14 @@ variable {R : Type _} [StrictOrderedCommRing R]
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
 @[simp]
-protected theorem Orientation.map_neg {ι : Type _} [DecidableEq ι] (f : M ≃ₗ[R] N)
-    (x : Orientation R M ι) : Orientation.map ι f (-x) = -Orientation.map ι f x :=
+protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
+    Orientation.map ι f (-x) = -Orientation.map ι f x :=
   Module.Ray.map_neg _ x
 #align orientation.map_neg Orientation.map_neg
 
 namespace Basis
 
-variable {ι : Type _} [DecidableEq ι]
+variable {ι : Type _}
 
 /-- The value of `orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -138,6 +138,7 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
     (f : M ≃ₗ[R] M) : Orientation.map ι f x = f.det⁻¹ • x :=
   by
   cases nonempty_fintype ι
+  letI := Classical.decEq ι
   induction' x using Module.Ray.ind with g hg
   rw [Orientation.map_apply, smul_rayOfNeZero, ray_eq_iff, Units.smul_def,
     (g.comp_linear_map ↑f.symm).eq_smul_basis_det e, g.eq_smul_basis_det e,
@@ -145,7 +146,7 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
     mul_one, smul_eq_mul, mul_comm, mul_smul, LinearEquiv.coe_inv_det]
 #align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smul
 
-variable [Fintype ι]
+variable [Fintype ι] [DecidableEq ι]
 
 /-- The orientation given by a basis. -/
 protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι :=
@@ -188,7 +189,7 @@ variable {R : Type _} [LinearOrderedCommRing R]
 
 variable {M : Type _} [AddCommGroup M] [Module R M]
 
-variable {ι : Type _} [DecidableEq ι]
+variable {ι : Type _}
 
 namespace Orientation
 
@@ -217,7 +218,7 @@ end Orientation
 
 namespace Basis
 
-variable [Fintype ι]
+variable [Fintype ι] [DecidableEq ι]
 
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
@@ -335,7 +336,7 @@ variable {R : Type _} [LinearOrderedField R]
 
 variable {M : Type _} [AddCommGroup M] [Module R M]
 
-variable {ι : Type _} [DecidableEq ι]
+variable {ι : Type _}
 
 namespace Orientation
 
@@ -351,6 +352,7 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
     x₁ = x₂ ∨ x₁ = -x₂ :=
   by
   have e := (fin_basis R M).reindex (Fintype.equivFinOfCardEq h).symm
+  letI := Classical.decEq ι
   rcases e.orientation_eq_or_eq_neg x₁ with (h₁ | h₁) <;>
       rcases e.orientation_eq_or_eq_neg x₂ with (h₂ | h₂) <;>
     simp [h₁, h₂]
@@ -416,14 +418,14 @@ include _i
 
 /-- If the index type has cardinality equal to the finite dimension, a basis with the given
 orientation. -/
-def someBasis [Nonempty ι] (x : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
-    Basis ι R M :=
+def someBasis [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
+    (h : Fintype.card ι = finrank R M) : Basis ι R M :=
   ((finBasis R M).reindex (Fintype.equivFinOfCardEq h).symm).adjustToOrientation x
 #align orientation.some_basis Orientation.someBasis
 
 /-- `some_basis` gives a basis with the required orientation. -/
 @[simp]
-theorem someBasis_orientation [Nonempty ι] (x : Orientation R M ι)
+theorem someBasis_orientation [Nonempty ι] [DecidableEq ι] (x : Orientation R M ι)
     (h : Fintype.card ι = finrank R M) : (x.someBasis h).Orientation = x :=
   Basis.orientation_adjustToOrientation _ _
 #align orientation.some_basis_orientation Orientation.someBasis_orientation

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

@@ -168,13 +168,13 @@ theorem orientation_unitsSmul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
   simp
 #align basis.orientation_units_smul Basis.orientation_unitsSmul
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]] -/
 @[simp]
 theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
     b.Orientation = positiveOrientation :=
   by
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ray_of_ne_zero _ _ _]]"
   convert b.det_is_empty
 #align basis.orientation_is_empty Basis.orientation_isEmpty
 

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

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)

@@ -41,11 +41,8 @@ open BigOperators
 section OrderedCommSemiring
 
 variable (R : Type*) [StrictOrderedCommSemiring R]
-
 variable (M : Type*) [AddCommMonoid M] [Module R M]
-
 variable {N : Type*} [AddCommMonoid N] [Module R N]
-
 variable (ι ι' : Type*)
 
 /-- An orientation of a module, intended to be used when `ι` is a `Fintype` with the same
@@ -143,7 +140,6 @@ end OrderedCommSemiring
 section OrderedCommRing
 
 variable {R : Type*} [StrictOrderedCommRing R]
-
 variable {M N : Type*} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
 @[simp]
@@ -220,9 +216,7 @@ end OrderedCommRing
 section LinearOrderedCommRing
 
 variable {R : Type*} [LinearOrderedCommRing R]
-
 variable {M : Type*} [AddCommGroup M] [Module R M]
-
 variable {ι : Type*}
 
 namespace Orientation
@@ -363,9 +357,7 @@ end LinearOrderedCommRing
 section LinearOrderedField
 
 variable {R : Type*} [LinearOrderedField R]
-
 variable {M : Type*} [AddCommGroup M] [Module R M]
-
 variable {ι : Type*}
 
 namespace Orientation

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

@@ -50,7 +50,7 @@ variable (ι ι' : Type*)
 
 /-- An orientation of a module, intended to be used when `ι` is a `Fintype` with the same
 cardinality as a basis. -/
-abbrev Orientation := Module.Ray R (M [Λ^ι]→ₗ[R] R)
+abbrev Orientation := Module.Ray R (M [⋀^ι]→ₗ[R] R)
 #align orientation Orientation
 
 /-- A type class fixing an orientation of a module. -/
@@ -69,7 +69,7 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 #align orientation.map Orientation.map
 
 @[simp]
-theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : M [Λ^ι]→ₗ[R] R) (hv : v ≠ 0) :
+theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : M [⋀^ι]→ₗ[R] R) (hv : v ≠ 0) :
     Orientation.map ι e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.compLinearMap e.symm) (mt (v.compLinearEquiv_eq_zero_iff e.symm).mp hv) :=
   rfl
@@ -95,7 +95,7 @@ def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R
 #align orientation.reindex Orientation.reindex
 
 @[simp]
-theorem Orientation.reindex_apply (e : ι ≃ ι') (v : M [Λ^ι]→ₗ[R] R) (hv : v ≠ 0) :
+theorem Orientation.reindex_apply (e : ι ≃ ι') (v : M [⋀^ι]→ₗ[R] R) (hv : v ≠ 0) :
     Orientation.reindex R M e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.domDomCongr e) (mt (v.domDomCongr_eq_zero_iff e).mp hv) :=
   rfl
@@ -237,7 +237,7 @@ theorem eq_or_eq_neg_of_isEmpty [IsEmpty ι] (o : Orientation R M ι) :
   simp only [ray_eq_iff, sameRay_neg_swap]
   rw [sameRay_or_sameRay_neg_iff_not_linearIndependent]
   intro h
-  set f : (M [Λ^ι]→ₗ[R] R) ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
+  set f : (M [⋀^ι]→ₗ[R] R) ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
   have H : LinearIndependent R ![f x, 1] := by
     convert h.map' f.toLinearMap f.ker
     ext i

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

@@ -241,7 +241,7 @@ theorem eq_or_eq_neg_of_isEmpty [IsEmpty ι] (o : Orientation R M ι) :
   have H : LinearIndependent R ![f x, 1] := by
     convert h.map' f.toLinearMap f.ker
     ext i
-    fin_cases i <;> simp
+    fin_cases i <;> simp [f]
   rw [linearIndependent_iff'] at H
   simpa using H Finset.univ ![1, -f x] (by simp [Fin.sum_univ_succ]) 0 (by simp)
 #align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmpty

Rename lemmas to enable new-style dot notation or drop repeating FiniteDimensional.finiteDimensional_*. Restore old names as deprecated aliases.

@@ -427,7 +427,7 @@ theorem map_eq_neg_iff_det_neg (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   have H : 0 < finrank R M := by
     rw [← h]
     exact Fintype.card_pos
-  haveI : FiniteDimensional R M := finiteDimensional_of_finrank H
+  haveI : FiniteDimensional R M := of_finrank_pos H
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_neg_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_neg_iff_det_neg Orientation.map_eq_neg_iff_det_neg
 

Rationale: this instance creates (empty) data out of nothing, which may conflict with other data. If you have in the context [Fintype i] and case on whether i is empty or not, then this gave two non-defeq instances of [Fintype i] around.

@@ -410,9 +410,7 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
     (h : Fintype.card ι = finrank R M) :
     Orientation.map ι f x = x ↔ 0 < LinearMap.det (f : M →ₗ[R] M) := by
   cases isEmpty_or_nonempty ι
-  · have H : finrank R M = 0 := by
-      refine' h.symm.trans _
-      convert @Fintype.card_of_isEmpty ι _
+  · have H : finrank R M = 0 := h.symm.trans Fintype.card_eq_zero
     simp [LinearMap.det_eq_one_of_finrank_eq_zero H]
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_self_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
@@ -424,9 +422,7 @@ theorem map_eq_neg_iff_det_neg (x : Orientation R M ι) (f : M ≃ₗ[R] M)
     (h : Fintype.card ι = finrank R M) :
     Orientation.map ι f x = -x ↔ LinearMap.det (f : M →ₗ[R] M) < 0 := by
   cases isEmpty_or_nonempty ι
-  · have H : finrank R M = 0 := by
-      refine' h.symm.trans _
-      convert @Fintype.card_of_isEmpty ι _
+  · have H : finrank R M = 0 := h.symm.trans Fintype.card_eq_zero
     simp [LinearMap.det_eq_one_of_finrank_eq_zero H, Module.Ray.ne_neg_self x]
   have H : 0 < finrank R M := by
     rw [← h]

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

@@ -50,7 +50,7 @@ variable (ι ι' : Type*)
 
 /-- An orientation of a module, intended to be used when `ι` is a `Fintype` with the same
 cardinality as a basis. -/
-abbrev Orientation := Module.Ray R (AlternatingMap R M R ι)
+abbrev Orientation := Module.Ray R (M [Λ^ι]→ₗ[R] R)
 #align orientation Orientation
 
 /-- A type class fixing an orientation of a module. -/
@@ -69,7 +69,7 @@ def Orientation.map (e : M ≃ₗ[R] N) : Orientation R M ι ≃ Orientation R N
 #align orientation.map Orientation.map
 
 @[simp]
-theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
+theorem Orientation.map_apply (e : M ≃ₗ[R] N) (v : M [Λ^ι]→ₗ[R] R) (hv : v ≠ 0) :
     Orientation.map ι e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.compLinearMap e.symm) (mt (v.compLinearEquiv_eq_zero_iff e.symm).mp hv) :=
   rfl
@@ -91,11 +91,11 @@ variable (R M) {ι ι'}
 
 /-- An equivalence between indices implies an equivalence between orientations. -/
 def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R M ι' :=
-  Module.Ray.map <| AlternatingMap.domDomLcongr R e
+  Module.Ray.map <| AlternatingMap.domDomCongrₗ R e
 #align orientation.reindex Orientation.reindex
 
 @[simp]
-theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
+theorem Orientation.reindex_apply (e : ι ≃ ι') (v : M [Λ^ι]→ₗ[R] R) (hv : v ≠ 0) :
     Orientation.reindex R M e (rayOfNeZero _ v hv) =
       rayOfNeZero _ (v.domDomCongr e) (mt (v.domDomCongr_eq_zero_iff e).mp hv) :=
   rfl
@@ -103,7 +103,7 @@ theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι)
 
 @[simp]
 theorem Orientation.reindex_refl : (Orientation.reindex R M <| Equiv.refl ι) = Equiv.refl _ := by
-  rw [Orientation.reindex, AlternatingMap.domDomLcongr_refl, Module.Ray.map_refl]
+  rw [Orientation.reindex, AlternatingMap.domDomCongrₗ_refl, Module.Ray.map_refl]
 #align orientation.reindex_refl Orientation.reindex_refl
 
 @[simp]
@@ -237,7 +237,7 @@ theorem eq_or_eq_neg_of_isEmpty [IsEmpty ι] (o : Orientation R M ι) :
   simp only [ray_eq_iff, sameRay_neg_swap]
   rw [sameRay_or_sameRay_neg_iff_not_linearIndependent]
   intro h
-  set f : AlternatingMap R M R ι ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
+  set f : (M [Λ^ι]→ₗ[R] R) ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
   have H : LinearIndependent R ![f x, 1] := by
     convert h.map' f.toLinearMap f.ker
     ext i

These can be inferred from [StrictOrderedSemiring R].

@@ -115,14 +115,14 @@ theorem Orientation.reindex_symm (e : ι ≃ ι') :
 end Reindex
 
 /-- A module is canonically oriented with respect to an empty index type. -/
-instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι where
+instance (priority := 100) IsEmpty.oriented [IsEmpty ι] : Module.Oriented R M ι where
   positiveOrientation :=
     rayOfNeZero R (AlternatingMap.constLinearEquivOfIsEmpty 1) <|
       AlternatingMap.constLinearEquivOfIsEmpty.injective.ne (by exact one_ne_zero)
 #align is_empty.oriented IsEmpty.oriented
 
 @[simp]
-theorem Orientation.map_positiveOrientation_of_isEmpty [Nontrivial R] [IsEmpty ι] (f : M ≃ₗ[R] N) :
+theorem Orientation.map_positiveOrientation_of_isEmpty [IsEmpty ι] (f : M ≃ₗ[R] N) :
     Orientation.map ι f positiveOrientation = positiveOrientation := rfl
 #align orientation.map_positive_orientation_of_is_empty Orientation.map_positiveOrientation_of_isEmpty
 
@@ -180,23 +180,23 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
 variable [Fintype ι] [DecidableEq ι] [Fintype ι'] [DecidableEq ι']
 
 /-- The orientation given by a basis. -/
-protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι :=
+protected def orientation (e : Basis ι R M) : Orientation R M ι :=
   rayOfNeZero R _ e.det_ne_zero
 #align basis.orientation Basis.orientation
 
-theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
+theorem orientation_map (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).orientation = Orientation.map ι f e.orientation := by
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
 #align basis.orientation_map Basis.orientation_map
 
-theorem orientation_reindex [Nontrivial R] (e : Basis ι R M) (eι : ι ≃ ι') :
+theorem orientation_reindex (e : Basis ι R M) (eι : ι ≃ ι') :
     (e.reindex eι).orientation = Orientation.reindex R M eι e.orientation := by
   simp_rw [Basis.orientation, Orientation.reindex_apply, Basis.det_reindex']
 #align basis.orientation_reindex Basis.orientation_reindex
 
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
-theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :
+theorem orientation_unitsSMul (e : Basis ι R M) (w : ι → Units R) :
     (e.unitsSMul w).orientation = (∏ i, w i)⁻¹ • e.orientation := by
   rw [Basis.orientation, Basis.orientation, smul_rayOfNeZero, ray_eq_iff,
     e.det.eq_smul_basis_det (e.unitsSMul w), det_unitsSMul_self, Units.smul_def, smul_smul]
@@ -206,7 +206,7 @@ theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
 #align basis.orientation_units_smul Basis.orientation_unitsSMul
 
 @[simp]
-theorem orientation_isEmpty [Nontrivial R] [IsEmpty ι] (b : Basis ι R M) :
+theorem orientation_isEmpty [IsEmpty ι] (b : Basis ι R M) :
     b.orientation = positiveOrientation := by
   rw [Basis.orientation]
   congr
@@ -230,7 +230,7 @@ namespace Orientation
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
 mathematical sense if `M` is zero-dimensional.) -/
-theorem eq_or_eq_neg_of_isEmpty [Nontrivial R] [IsEmpty ι] (o : Orientation R M ι) :
+theorem eq_or_eq_neg_of_isEmpty [IsEmpty ι] (o : Orientation R M ι) :
     o = positiveOrientation ∨ o = -positiveOrientation := by
   induction' o using Module.Ray.ind with x hx
   dsimp [positiveOrientation]
@@ -300,7 +300,7 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
 @[simp]
-theorem orientation_neg_single [Nontrivial R] (e : Basis ι R M) (i : ι) :
+theorem orientation_neg_single (e : Basis ι R M) (i : ι) :
     (e.unitsSMul (Function.update 1 i (-1))).orientation = -e.orientation := by
   rw [orientation_unitsSMul, Finset.prod_update_of_mem (Finset.mem_univ _)]
   simp
@@ -308,7 +308,7 @@ theorem orientation_neg_single [Nontrivial R] (e : Basis ι R M) (i : ι) :
 
 /-- Given a basis and an orientation, return a basis giving that orientation: either the original
 basis, or one constructed by negating a single (arbitrary) basis vector. -/
-def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Orientation R M ι) :
+def adjustToOrientation [Nonempty ι] (e : Basis ι R M) (x : Orientation R M ι) :
     Basis ι R M :=
   haveI := Classical.decEq (Orientation R M ι)
   if e.orientation = x then e else e.unitsSMul (Function.update 1 (Classical.arbitrary ι) (-1))
@@ -316,7 +316,7 @@ def adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M) (x : Ori
 
 /-- `adjust_to_orientation` gives a basis with the required orientation. -/
 @[simp]
-theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
+theorem orientation_adjustToOrientation [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) : (e.adjustToOrientation x).orientation = x := by
   rw [adjustToOrientation]
   split_ifs with h
@@ -327,7 +327,7 @@ theorem orientation_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis
 
 /-- Every basis vector from `adjust_to_orientation` is either that from the original basis or its
 negation. -/
-theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
+theorem adjustToOrientation_apply_eq_or_eq_neg [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (i : ι) :
     e.adjustToOrientation x i = e i ∨ e.adjustToOrientation x i = -e i := by
   rw [adjustToOrientation]
@@ -336,7 +336,7 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
   · by_cases hi : i = Classical.arbitrary ι <;> simp [unitsSMul_apply, hi]
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
 
-theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
+theorem det_adjustToOrientation [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
     (e.adjustToOrientation x).det = e.det ∨ (e.adjustToOrientation x).det = -e.det := by
   dsimp [Basis.adjustToOrientation]
@@ -351,7 +351,7 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
 
 @[simp]
-theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
+theorem abs_det_adjustToOrientation [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (v : ι → M) : |(e.adjustToOrientation x).det v| = |e.det v| := by
   cases' e.det_adjustToOrientation x with h h <;> simp [h]
 #align basis.abs_det_adjust_to_orientation Basis.abs_det_adjustToOrientation

Removes nonterminal simps on lines looking like simp [...]

@@ -344,7 +344,8 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
   · left
     rfl
   · right
-    simp [e.det_unitsSMul, ← Units.coe_prod, Finset.prod_update_of_mem]
+    simp only [e.det_unitsSMul, ne_eq, Finset.mem_univ, Finset.prod_update_of_mem, not_true,
+      Pi.one_apply, Finset.prod_const_one, mul_one, inv_neg', inv_one, Units.val_neg, Units.val_one]
     ext
     simp
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation

Fixes the nonterminal simps identified by #7496

@@ -201,7 +201,7 @@ theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Unit
   rw [Basis.orientation, Basis.orientation, smul_rayOfNeZero, ray_eq_iff,
     e.det.eq_smul_basis_det (e.unitsSMul w), det_unitsSMul_self, Units.smul_def, smul_smul]
   norm_cast
-  simp
+  simp only [mul_left_inv, Units.val_one, one_smul]
   exact SameRay.rfl
 #align basis.orientation_units_smul Basis.orientation_unitsSMul
 

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

@@ -397,7 +397,7 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
 /-- The value of `Orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
 theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
-  (h : Fintype.card ι = finrank R M) : Orientation.map ι f x = (LinearEquiv.det f)⁻¹ • x :=
+    (h : Fintype.card ι = finrank R M) : Orientation.map ι f x = (LinearEquiv.det f)⁻¹ • x :=
   haveI e := (finBasis R M).reindex (Fintype.equivFinOfCardEq h).symm
   e.map_orientation_eq_det_inv_smul x f
 #align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smul

@@ -115,8 +115,8 @@ theorem Orientation.reindex_symm (e : ι ≃ ι') :
 end Reindex
 
 /-- A module is canonically oriented with respect to an empty index type. -/
-instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι
-    where positiveOrientation :=
+instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι where
+  positiveOrientation :=
     rayOfNeZero R (AlternatingMap.constLinearEquivOfIsEmpty 1) <|
       AlternatingMap.constLinearEquivOfIsEmpty.injective.ne (by exact one_ne_zero)
 #align is_empty.oriented IsEmpty.oriented

This forward-ports leanprover-community/mathlib#19236

@@ -6,7 +6,7 @@ Authors: Joseph Myers
 import Mathlib.LinearAlgebra.Ray
 import Mathlib.LinearAlgebra.Determinant
 
-#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"0c1d80f5a86b36c1db32e021e8d19ae7809d5b79"
 
 /-!
 # Orientations of modules
@@ -46,7 +46,7 @@ variable (M : Type*) [AddCommMonoid M] [Module R M]
 
 variable {N : Type*} [AddCommMonoid N] [Module R N]
 
-variable (ι : Type*)
+variable (ι ι' : Type*)
 
 /-- An orientation of a module, intended to be used when `ι` is a `Fintype` with the same
 cardinality as a basis. -/
@@ -85,6 +85,35 @@ theorem Orientation.map_symm (e : M ≃ₗ[R] N) :
     (Orientation.map ι e).symm = Orientation.map ι e.symm := rfl
 #align orientation.map_symm Orientation.map_symm
 
+section Reindex
+
+variable (R M) {ι ι'}
+
+/-- An equivalence between indices implies an equivalence between orientations. -/
+def Orientation.reindex (e : ι ≃ ι') : Orientation R M ι ≃ Orientation R M ι' :=
+  Module.Ray.map <| AlternatingMap.domDomLcongr R e
+#align orientation.reindex Orientation.reindex
+
+@[simp]
+theorem Orientation.reindex_apply (e : ι ≃ ι') (v : AlternatingMap R M R ι) (hv : v ≠ 0) :
+    Orientation.reindex R M e (rayOfNeZero _ v hv) =
+      rayOfNeZero _ (v.domDomCongr e) (mt (v.domDomCongr_eq_zero_iff e).mp hv) :=
+  rfl
+#align orientation.reindex_apply Orientation.reindex_apply
+
+@[simp]
+theorem Orientation.reindex_refl : (Orientation.reindex R M <| Equiv.refl ι) = Equiv.refl _ := by
+  rw [Orientation.reindex, AlternatingMap.domDomLcongr_refl, Module.Ray.map_refl]
+#align orientation.reindex_refl Orientation.reindex_refl
+
+@[simp]
+theorem Orientation.reindex_symm (e : ι ≃ ι') :
+    (Orientation.reindex R M e).symm = Orientation.reindex R M e.symm :=
+  rfl
+#align orientation.reindex_symm Orientation.reindex_symm
+
+end Reindex
+
 /-- A module is canonically oriented with respect to an empty index type. -/
 instance (priority := 100) IsEmpty.oriented [Nontrivial R] [IsEmpty ι] : Module.Oriented R M ι
     where positiveOrientation :=
@@ -123,9 +152,15 @@ protected theorem Orientation.map_neg {ι : Type*} (f : M ≃ₗ[R] N) (x : Orie
   Module.Ray.map_neg _ x
 #align orientation.map_neg Orientation.map_neg
 
+@[simp]
+protected theorem Orientation.reindex_neg {ι ι' : Type*} (e : ι ≃ ι') (x : Orientation R M ι) :
+    Orientation.reindex R M e (-x) = -Orientation.reindex R M e x :=
+  Module.Ray.map_neg _ x
+#align orientation.reindex_neg Orientation.reindex_neg
+
 namespace Basis
 
-variable {ι : Type*}
+variable {ι ι' : Type*}
 
 /-- The value of `Orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -142,7 +177,7 @@ theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orie
     LinearEquiv.coe_inv_det]
 #align basis.map_orientation_eq_det_inv_smul Basis.map_orientation_eq_det_inv_smul
 
-variable [Fintype ι] [DecidableEq ι]
+variable [Fintype ι] [DecidableEq ι] [Fintype ι'] [DecidableEq ι']
 
 /-- The orientation given by a basis. -/
 protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι :=
@@ -154,6 +189,11 @@ theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
 #align basis.orientation_map Basis.orientation_map
 
+theorem orientation_reindex [Nontrivial R] (e : Basis ι R M) (eι : ι ≃ ι') :
+    (e.reindex eι).orientation = Orientation.reindex R M eι e.orientation := by
+  simp_rw [Basis.orientation, Orientation.reindex_apply, Basis.det_reindex']
+#align basis.orientation_reindex Basis.orientation_reindex
+
 /-- The orientation given by a basis derived using `units_smul`, in terms of the product of those
 units. -/
 theorem orientation_unitsSMul [Nontrivial R] (e : Basis ι R M) (w : ι → Units R) :

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

This has nice performance benefits.

@@ -40,13 +40,13 @@ open BigOperators
 
 section OrderedCommSemiring
 
-variable (R : Type _) [StrictOrderedCommSemiring R]
+variable (R : Type*) [StrictOrderedCommSemiring R]
 
-variable (M : Type _) [AddCommMonoid M] [Module R M]
+variable (M : Type*) [AddCommMonoid M] [Module R M]
 
-variable {N : Type _} [AddCommMonoid N] [Module R N]
+variable {N : Type*} [AddCommMonoid N] [Module R N]
 
-variable (ι : Type _)
+variable (ι : Type*)
 
 /-- An orientation of a module, intended to be used when `ι` is a `Fintype` with the same
 cardinality as a basis. -/
@@ -113,19 +113,19 @@ end OrderedCommSemiring
 
 section OrderedCommRing
 
-variable {R : Type _} [StrictOrderedCommRing R]
+variable {R : Type*} [StrictOrderedCommRing R]
 
-variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
+variable {M N : Type*} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
 @[simp]
-protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
+protected theorem Orientation.map_neg {ι : Type*} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
     Orientation.map ι f (-x) = -Orientation.map ι f x :=
   Module.Ray.map_neg _ x
 #align orientation.map_neg Orientation.map_neg
 
 namespace Basis
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 /-- The value of `Orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
@@ -179,11 +179,11 @@ end OrderedCommRing
 
 section LinearOrderedCommRing
 
-variable {R : Type _} [LinearOrderedCommRing R]
+variable {R : Type*} [LinearOrderedCommRing R]
 
-variable {M : Type _} [AddCommGroup M] [Module R M]
+variable {M : Type*} [AddCommGroup M] [Module R M]
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 namespace Orientation
 
@@ -321,11 +321,11 @@ end LinearOrderedCommRing
 
 section LinearOrderedField
 
-variable {R : Type _} [LinearOrderedField R]
+variable {R : Type*} [LinearOrderedField R]
 
-variable {M : Type _} [AddCommGroup M] [Module R M]
+variable {M : Type*} [AddCommGroup M] [Module R M]
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 namespace Orientation
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.orientation
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Ray
 import Mathlib.LinearAlgebra.Determinant
 
+#align_import linear_algebra.orientation from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+
 /-!
 # Orientations of modules
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -344,7 +344,7 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
   letI := Classical.decEq ι
   -- Porting note: this needs to be made explicit for the simp below
   have orientation_neg_neg :
-    ∀ f : Basis ι R M,  - -Basis.orientation f = Basis.orientation f := by simp
+    ∀ f : Basis ι R M, - -Basis.orientation f = Basis.orientation f := by simp
   rcases e.orientation_eq_or_eq_neg x₁ with (h₁ | h₁) <;>
     rcases e.orientation_eq_or_eq_neg x₂ with (h₂ | h₂) <;> simp [h₁, h₂, orientation_neg_neg]
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg

Forward-port leanprover-community/mathlib#19123

@@ -200,14 +200,13 @@ theorem eq_or_eq_neg_of_isEmpty [Nontrivial R] [IsEmpty ι] (o : Orientation R M
   simp only [ray_eq_iff, sameRay_neg_swap]
   rw [sameRay_or_sameRay_neg_iff_not_linearIndependent]
   intro h
-  let a : R := AlternatingMap.constLinearEquivOfIsEmpty.symm x
-  have H : LinearIndependent R ![a, 1] := by
-    let f := (@AlternatingMap.constLinearEquivOfIsEmpty ι R M R _ _ _ _ _ _).symm
-    rw [show ![a, 1] = (f.toLinearMap ∘ ![x, AlternatingMap.constOfIsEmpty R M 1])
-      by (ext i ; fin_cases i <;> simp)]
-    exact h.map' f.toLinearMap f.ker
+  set f : AlternatingMap R M R ι ≃ₗ[R] R := AlternatingMap.constLinearEquivOfIsEmpty.symm
+  have H : LinearIndependent R ![f x, 1] := by
+    convert h.map' f.toLinearMap f.ker
+    ext i
+    fin_cases i <;> simp
   rw [linearIndependent_iff'] at H
-  simpa using H Finset.univ ![1, -a] (by simp [Fin.sum_univ_succ]) 0 (by simp)
+  simpa using H Finset.univ ![1, -f x] (by simp [Fin.sum_univ_succ]) 0 (by simp)
 #align orientation.eq_or_eq_neg_of_is_empty Orientation.eq_or_eq_neg_of_isEmpty
 
 end Orientation

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -120,8 +120,6 @@ variable {R : Type _} [StrictOrderedCommRing R]
 
 variable {M N : Type _} [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
 
-set_option maxHeartbeats 400000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 @[simp]
 protected theorem Orientation.map_neg {ι : Type _} (f : M ≃ₗ[R] N) (x : Orientation R M ι) :
     Orientation.map ι f (-x) = -Orientation.map ι f x :=
@@ -132,7 +130,6 @@ namespace Basis
 
 variable {ι : Type _}
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- The value of `Orientation.map` when the index type has the cardinality of a basis, in terms
 of `f.det`. -/
 theorem map_orientation_eq_det_inv_smul [Finite ι] (e : Basis ι R M) (x : Orientation R M ι)
@@ -155,7 +152,6 @@ protected def orientation [Nontrivial R] (e : Basis ι R M) : Orientation R M ι
   rayOfNeZero R _ e.det_ne_zero
 #align basis.orientation Basis.orientation
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem orientation_map [Nontrivial R] (e : Basis ι R M) (f : M ≃ₗ[R] N) :
     (e.map f).orientation = Orientation.map ι f e.orientation := by
   simp_rw [Basis.orientation, Orientation.map_apply, Basis.det_map']
@@ -194,8 +190,6 @@ variable {ι : Type _}
 
 namespace Orientation
 
-set_option maxHeartbeats 350000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- A module `M` over a linearly ordered commutative ring has precisely two "orientations" with
 respect to an empty index type. (Note that these are only orientations of `M` of in the conventional
 mathematical sense if `M` is zero-dimensional.) -/
@@ -222,7 +216,6 @@ namespace Basis
 
 variable [Fintype ι] [DecidableEq ι]
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- The orientations given by two bases are equal if and only if the determinant of one basis
 with respect to the other is positive. -/
 theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
@@ -234,8 +227,6 @@ theorem orientation_eq_iff_det_pos (e₁ e₂ : Basis ι R M) :
 
 #align basis.orientation_eq_iff_det_pos Basis.orientation_eq_iff_det_pos
 
-set_option maxHeartbeats 300000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- Given a basis, any orientation equals the orientation given by that basis or its negation. -/
 theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     x = e.orientation ∨ x = -e.orientation := by
@@ -246,7 +237,6 @@ theorem orientation_eq_or_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     lt_or_lt_iff_ne, ne_comm]
 #align basis.orientation_eq_or_eq_neg Basis.orientation_eq_or_eq_neg
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- Given a basis, an orientation equals the negation of that given by that basis if and only
 if it does not equal that given by that basis. -/
 theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
@@ -255,8 +245,6 @@ theorem orientation_ne_iff_eq_neg (e : Basis ι R M) (x : Orientation R M ι) :
     h.symm ▸ (Module.Ray.ne_neg_self e.orientation).symm⟩
 #align basis.orientation_ne_iff_eq_neg Basis.orientation_ne_iff_eq_neg
 
-set_option maxHeartbeats 250000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- Composing a basis with a linear equiv gives the same orientation if and only if the
 determinant is positive. -/
 theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -265,8 +253,6 @@ theorem orientation_comp_linearEquiv_eq_iff_det_pos (e : Basis ι R M) (f : M 
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_iff_det_pos Basis.orientation_comp_linearEquiv_eq_iff_det_pos
 
-set_option maxHeartbeats 350000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- Composing a basis with a linear equiv gives the negation of that orientation if and only if
 the determinant is negative. -/
 theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f : M ≃ₗ[R] M) :
@@ -275,8 +261,6 @@ theorem orientation_comp_linearEquiv_eq_neg_iff_det_neg (e : Basis ι R M) (f :
     LinearEquiv.coe_det]
 #align basis.orientation_comp_linear_equiv_eq_neg_iff_det_neg Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg
 
-set_option maxHeartbeats 300000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- Negating a single basis vector (represented using `units_smul`) negates the corresponding
 orientation. -/
 @[simp]
@@ -316,7 +300,6 @@ theorem adjustToOrientation_apply_eq_or_eq_neg [Nontrivial R] [Nonempty ι] (e :
   · by_cases hi : i = Classical.arbitrary ι <;> simp [unitsSMul_apply, hi]
 #align basis.adjust_to_orientation_apply_eq_or_eq_neg Basis.adjustToOrientation_apply_eq_or_eq_neg
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) :
     (e.adjustToOrientation x).det = e.det ∨ (e.adjustToOrientation x).det = -e.det := by
@@ -330,7 +313,6 @@ theorem det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     simp
 #align basis.det_adjust_to_orientation Basis.det_adjustToOrientation
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 @[simp]
 theorem abs_det_adjustToOrientation [Nontrivial R] [Nonempty ι] (e : Basis ι R M)
     (x : Orientation R M ι) (v : ι → M) : |(e.adjustToOrientation x).det v| = |e.det v| := by
@@ -355,9 +337,6 @@ variable [Fintype ι] [_i : FiniteDimensional R M]
 
 open FiniteDimensional
 
-set_option maxHeartbeats 350000 in -- Porting note: added
-set_option synthInstance.maxHeartbeats 25000 in -- Porting note : added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- If the index type has cardinality equal to the finite dimension, any two orientations are
 equal or negations. -/
 theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -371,7 +350,6 @@ theorem eq_or_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fin
     rcases e.orientation_eq_or_eq_neg x₂ with (h₂ | h₂) <;> simp [h₁, h₂, orientation_neg_neg]
 #align orientation.eq_or_eq_neg Orientation.eq_or_eq_neg
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- If the index type has cardinality equal to the finite dimension, an orientation equals the
 negation of another orientation if and only if they are not equal. -/
 theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = finrank R M) :
@@ -380,8 +358,6 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
     he.symm ▸ (Module.Ray.ne_neg_self x₂).symm⟩
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
 
-set_option synthInstance.maxHeartbeats 50000 in -- Porting note : added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- The value of `Orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/
 theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
@@ -390,8 +366,6 @@ theorem map_eq_det_inv_smul (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   e.map_orientation_eq_det_inv_smul x f
 #align orientation.map_eq_det_inv_smul Orientation.map_eq_det_inv_smul
 
-set_option maxHeartbeats 350000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the same orientation if and only if the
 determinant is positive. -/
@@ -406,8 +380,6 @@ theorem map_eq_iff_det_pos (x : Orientation R M ι) (f : M ≃ₗ[R] M)
   rw [map_eq_det_inv_smul _ _ h, units_inv_smul, units_smul_eq_self_iff, LinearEquiv.coe_det]
 #align orientation.map_eq_iff_det_pos Orientation.map_eq_iff_det_pos
 
-set_option maxHeartbeats 550000 in -- Porting note: added
-set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- If the index type has cardinality equal to the finite dimension, composing an alternating
 map with the same linear equiv on each argument gives the negation of that orientation if and
 only if the determinant is negative. -/

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

@@ -380,7 +380,7 @@ theorem ne_iff_eq_neg (x₁ x₂ : Orientation R M ι) (h : Fintype.card ι = fi
     he.symm ▸ (Module.Ray.ne_neg_self x₂).symm⟩
 #align orientation.ne_iff_eq_neg Orientation.ne_iff_eq_neg
 
-set_option synthInstance.maxHeartbeats 30000 in -- Porting note : added
+set_option synthInstance.maxHeartbeats 50000 in -- Porting note : added
 set_option synthInstance.etaExperiment true in -- Porting note: added
 /-- The value of `Orientation.map` when the index type has cardinality equal to the finite
 dimension, in terms of `f.det`. -/

I had to add a bunch of set_option synthInstance.etaExperiment true, set_option maxHeartbeats and set_option synthInstance.maxHeartbeats to this file

I tried to use the methods described in this Zulip thread to remove some of the maxHeartbeats but I was not successful.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>