linear_algebra.affine_space.basis ⟷ Mathlib.LinearAlgebra.AffineSpace.Basis

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

@@ -358,7 +358,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 #print AffineBasis.exists_affine_subbasis /-
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=

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

@@ -273,7 +273,7 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
     ∑ i, b.Coord i v • b i = v :=
   by
   have hb := b.affine_combination_coord_eq_self v
-  rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb 
+  rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
 -/
 

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

@@ -196,7 +196,7 @@ theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCo
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   by
   ext
-  classical
+  classical simp [AffineBasis.coord]
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
 -/
 
@@ -225,14 +225,18 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 #print AffineBasis.coord_apply_combination_of_mem /-
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination k b w) = w i := by classical
+    b.Coord i (s.affineCombination k b w) = w i := by
+  classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_true,
+    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 -/
 
 #print AffineBasis.coord_apply_combination_of_not_mem /-
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination k b w) = 0 := by classical
+    b.Coord i (s.affineCombination k b w) = 0 := by
+  classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_false,
+    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 -/
 
@@ -301,7 +305,17 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
 -/
 
 #print AffineBasis.surjective_coord /-
-theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by classical
+theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
+  classical
+  intro x
+  obtain ⟨j, hij⟩ := exists_ne i
+  let s : Finset ι := {i, j}
+  have hi : i ∈ s := by simp
+  have hj : j ∈ s := by simp
+  let w : ι → k := fun j' => if j' = i then x else 1 - x
+  have hw : s.sum w = 1 := by simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
+  use s.affine_combination k b w
+  simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 -/
 

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

@@ -196,7 +196,7 @@ theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCo
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   by
   ext
-  classical simp [AffineBasis.coord]
+  classical
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
 -/
 
@@ -225,18 +225,14 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 #print AffineBasis.coord_apply_combination_of_mem /-
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination k b w) = w i := by
-  classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_true,
-    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
+    b.Coord i (s.affineCombination k b w) = w i := by classical
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 -/
 
 #print AffineBasis.coord_apply_combination_of_not_mem /-
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination k b w) = 0 := by
-  classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_false,
-    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
+    b.Coord i (s.affineCombination k b w) = 0 := by classical
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 -/
 
@@ -305,17 +301,7 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
 -/
 
 #print AffineBasis.surjective_coord /-
-theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
-  classical
-  intro x
-  obtain ⟨j, hij⟩ := exists_ne i
-  let s : Finset ι := {i, j}
-  have hi : i ∈ s := by simp
-  have hj : j ∈ s := by simp
-  let w : ι → k := fun j' => if j' = i then x else 1 - x
-  have hw : s.sum w = 1 := by simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
-  use s.affine_combination k b w
-  simp [b.coord_apply_combination_of_mem hi hw]
+theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by classical
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 -/
 

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

@@ -73,12 +73,12 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i j : 
 instance : Inhabited (AffineBasis PUnit k PUnit) :=
   ⟨⟨id, affineIndependent_of_subsingleton k id, by simp⟩⟩
 
-#print AffineBasis.instDFunLike /-
-instance instDFunLike : DFunLike (AffineBasis ι k P) ι fun _ => P
+#print AffineBasis.instFunLike /-
+instance instFunLike : DFunLike (AffineBasis ι k P) ι fun _ => P
     where
   coe := AffineBasis.toFun
   coe_injective' f g h := by cases f <;> cases g <;> congr
-#align affine_basis.fun_like AffineBasis.instDFunLike
+#align affine_basis.fun_like AffineBasis.instFunLike
 -/
 
 #print AffineBasis.ext /-

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

@@ -73,18 +73,18 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i j : 
 instance : Inhabited (AffineBasis PUnit k PUnit) :=
   ⟨⟨id, affineIndependent_of_subsingleton k id, by simp⟩⟩
 
-#print AffineBasis.funLike /-
-instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P
+#print AffineBasis.instDFunLike /-
+instance instDFunLike : DFunLike (AffineBasis ι k P) ι fun _ => P
     where
   coe := AffineBasis.toFun
   coe_injective' f g h := by cases f <;> cases g <;> congr
-#align affine_basis.fun_like AffineBasis.funLike
+#align affine_basis.fun_like AffineBasis.instDFunLike
 -/
 
 #print AffineBasis.ext /-
 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=
-  FunLike.coe_injective h
+  DFunLike.coe_injective h
 #align affine_basis.ext AffineBasis.ext
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.LinearAlgebra.AffineSpace.Independent
-import Mathbin.LinearAlgebra.Basis
+import LinearAlgebra.AffineSpace.Independent
+import LinearAlgebra.Basis
 
 #align_import linear_algebra.affine_space.basis from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
 
@@ -358,7 +358,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 #print AffineBasis.exists_affine_subbasis /-
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.basis
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.AffineSpace.Independent
 import Mathbin.LinearAlgebra.Basis
 
+#align_import linear_algebra.affine_space.basis from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Affine bases and barycentric coordinates
 
@@ -361,7 +358,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 #print AffineBasis.exists_affine_subbasis /-
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=

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

@@ -76,8 +76,6 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i j : 
 instance : Inhabited (AffineBasis PUnit k PUnit) :=
   ⟨⟨id, affineIndependent_of_subsingleton k id, by simp⟩⟩
 
-include V
-
 #print AffineBasis.funLike /-
 instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P
     where
@@ -86,20 +84,24 @@ instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P
 #align affine_basis.fun_like AffineBasis.funLike
 -/
 
+#print AffineBasis.ext /-
 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=
   FunLike.coe_injective h
 #align affine_basis.ext AffineBasis.ext
+-/
 
+#print AffineBasis.ind /-
 theorem ind : AffineIndependent k b :=
   b.ind'
 #align affine_basis.ind AffineBasis.ind
+-/
 
+#print AffineBasis.tot /-
 theorem tot : affineSpan k (range b) = ⊤ :=
   b.tot'
 #align affine_basis.tot AffineBasis.tot
-
-include b
+-/
 
 #print AffineBasis.nonempty /-
 protected theorem nonempty : Nonempty ι :=
@@ -116,20 +118,26 @@ def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
 #align affine_basis.reindex AffineBasis.reindex
 -/
 
+#print AffineBasis.coe_reindex /-
 @[simp, norm_cast]
 theorem coe_reindex : ⇑(b.reindex e) = b ∘ e.symm :=
   rfl
 #align affine_basis.coe_reindex AffineBasis.coe_reindex
+-/
 
+#print AffineBasis.reindex_apply /-
 @[simp]
 theorem reindex_apply (i' : ι') : b.reindex e i' = b (e.symm i') :=
   rfl
 #align affine_basis.reindex_apply AffineBasis.reindex_apply
+-/
 
+#print AffineBasis.reindex_refl /-
 @[simp]
 theorem reindex_refl : b.reindex (Equiv.refl _) = b :=
   ext rfl
 #align affine_basis.reindex_refl AffineBasis.reindex_refl
+-/
 
 #print AffineBasis.basisOf /-
 /-- Given an affine basis for an affine space `P`, if we single out one member of the family, we
@@ -151,18 +159,23 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
 #align affine_basis.basis_of AffineBasis.basisOf
 -/
 
+#print AffineBasis.basisOf_apply /-
 @[simp]
 theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b ↑j -ᵥ b i := by
   simp [basis_of]
 #align affine_basis.basis_of_apply AffineBasis.basisOf_apply
+-/
 
+#print AffineBasis.basisOf_reindex /-
 @[simp]
 theorem basisOf_reindex (i : ι') :
     (b.reindex e).basisOf i =
       (b.basisOf <| e.symm i).reindex (e.subtypeEquiv fun _ => e.eq_symm_apply.Not) :=
   by ext j; simp
 #align affine_basis.basis_of_reindex AffineBasis.basisOf_reindex
+-/
 
+#print AffineBasis.coord /-
 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k
     where
@@ -172,49 +185,65 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k
     rw [vadd_vsub_assoc, LinearMap.map_add, vadd_eq_add, LinearMap.neg_apply,
       sub_add_eq_sub_sub_swap, add_comm, sub_eq_add_neg]
 #align affine_basis.coord AffineBasis.coord
+-/
 
+#print AffineBasis.linear_eq_sumCoords /-
 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCoords :=
   rfl
 #align affine_basis.linear_eq_sum_coords AffineBasis.linear_eq_sumCoords
+-/
 
+#print AffineBasis.coord_reindex /-
 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   by
   ext
   classical simp [AffineBasis.coord]
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
+-/
 
+#print AffineBasis.coord_apply_eq /-
 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
   simp only [coord, Basis.coe_sumCoords, LinearEquiv.map_zero, LinearEquiv.coe_coe, sub_zero,
     AffineMap.coe_mk, Finsupp.sum_zero_index, vsub_self]
 #align affine_basis.coord_apply_eq AffineBasis.coord_apply_eq
+-/
 
+#print AffineBasis.coord_apply_ne /-
 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
   rw [coord, AffineMap.coe_mk, ← Subtype.coe_mk j h.symm, ← b.basis_of_apply,
     Basis.sumCoords_self_apply, sub_self]
 #align affine_basis.coord_apply_ne AffineBasis.coord_apply_ne
+-/
 
+#print AffineBasis.coord_apply /-
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
 #align affine_basis.coord_apply AffineBasis.coord_apply
+-/
 
+#print AffineBasis.coord_apply_combination_of_mem /-
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = w i := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_true,
     mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
+-/
 
+#print AffineBasis.coord_apply_combination_of_not_mem /-
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = 0 := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_false,
     mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
+-/
 
+#print AffineBasis.sum_coord_apply_eq_one /-
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : ∑ i, b.Coord i q = 1 :=
   by
@@ -224,7 +253,9 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : ∑ i, b.Coord i q = 1 :=
   ext i
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_one
+-/
 
+#print AffineBasis.affineCombination_coord_eq_self /-
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
     (Finset.univ.affineCombination k b fun i => b.Coord i q) = q :=
@@ -235,7 +266,9 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
   ext i
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_self
+-/
 
+#print AffineBasis.linear_combination_coord_eq_self /-
 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
 @[simp]
@@ -245,14 +278,18 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
   have hb := b.affine_combination_coord_eq_self v
   rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb 
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
+-/
 
+#print AffineBasis.ext_elem /-
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
   cases nonempty_fintype ι
   rw [← b.affine_combination_coord_eq_self q₁, ← b.affine_combination_coord_eq_self q₂]
   simp only [h]
 #align affine_basis.ext_elem AffineBasis.ext_elem
+-/
 
+#print AffineBasis.coe_coord_of_subsingleton_eq_one /-
 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
   by
@@ -268,7 +305,9 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
   have hq : q = s.affine_combination k b (Function.const ι (1 : k)) := by simp
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_one
+-/
 
+#print AffineBasis.surjective_coord /-
 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
   intro x
@@ -281,7 +320,9 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
   use s.affine_combination k b w
   simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
+-/
 
+#print AffineBasis.coords /-
 /-- Barycentric coordinates as an affine map. -/
 noncomputable def coords : P →ᵃ[k] ι → k
     where
@@ -295,11 +336,14 @@ noncomputable def coords : P →ᵃ[k] ι → k
     simp only [linear_eq_sum_coords, LinearMap.coe_mk, LinearMap.neg_apply, Pi.vadd_apply',
       AffineMap.map_vadd]
 #align affine_basis.coords AffineBasis.coords
+-/
 
+#print AffineBasis.coords_apply /-
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
   rfl
 #align affine_basis.coords_apply AffineBasis.coords_apply
+-/
 
 end Ring
 
@@ -307,8 +351,7 @@ section DivisionRing
 
 variable [DivisionRing k] [Module k V]
 
-include V
-
+#print AffineBasis.coord_apply_centroid /-
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}
     (hi : i ∈ s) : b.Coord i (s.centroid k b) = (s.card : k)⁻¹ := by
@@ -316,8 +359,10 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
     b.coord_apply_combination_of_mem hi (s.sum_centroid_weights_eq_one_of_nonempty _ ⟨i, hi⟩),
     Finset.centroidWeights]
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+#print AffineBasis.exists_affine_subbasis /-
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=
   by
@@ -325,13 +370,16 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
   refine' ⟨s, hst, ⟨coe, h_ind, _⟩, rfl⟩
   rw [Subtype.range_coe, h_tot, ht]
 #align affine_basis.exists_affine_subbasis AffineBasis.exists_affine_subbasis
+-/
 
 variable (k V P)
 
+#print AffineBasis.exists_affineBasis /-
 theorem exists_affineBasis : ∃ (s : Set P) (b : AffineBasis (↥s) k P), ⇑b = coe :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)
   ⟨s, hs⟩
 #align affine_basis.exists_affine_basis AffineBasis.exists_affineBasis
+-/
 
 end DivisionRing
 

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

@@ -216,7 +216,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
 @[simp]
-theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
+theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : ∑ i, b.Coord i q = 1 :=
   by
   have hq : q ∈ affineSpan k (range b) := by rw [b.tot]; exact AffineSubspace.mem_top k V q
   obtain ⟨w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan_of_fintype hq
@@ -240,7 +240,7 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
 affine space is a module so we can talk about linear combinations. -/
 @[simp]
 theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (v : V) :
-    (∑ i, b.Coord i v • b i) = v :=
+    ∑ i, b.Coord i v • b i = v :=
   by
   have hb := b.affine_combination_coord_eq_self v
   rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -317,7 +317,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
     Finset.centroidWeights]
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=
   by

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

@@ -205,16 +205,14 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = w i := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_true,
-      mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq,
-      s.map_affine_combination b w hw]
+    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = 0 := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_false,
-      mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq,
-      s.map_affine_combination b w hw]
+    mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq, s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
 @[simp]
@@ -273,15 +271,15 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
 
 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
-    intro x
-    obtain ⟨j, hij⟩ := exists_ne i
-    let s : Finset ι := {i, j}
-    have hi : i ∈ s := by simp
-    have hj : j ∈ s := by simp
-    let w : ι → k := fun j' => if j' = i then x else 1 - x
-    have hw : s.sum w = 1 := by simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
-    use s.affine_combination k b w
-    simp [b.coord_apply_combination_of_mem hi hw]
+  intro x
+  obtain ⟨j, hij⟩ := exists_ne i
+  let s : Finset ι := {i, j}
+  have hi : i ∈ s := by simp
+  have hj : j ∈ s := by simp
+  let w : ι → k := fun j' => if j' = i then x else 1 - x
+  have hw : s.sum w = 1 := by simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
+  use s.affine_combination k b w
+  simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 
 /-- Barycentric coordinates as an affine map. -/

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

@@ -57,7 +57,7 @@ universe u₁ u₂ u₃ u₄
 /-- An affine basis is a family of affine-independent points whose span is the top subspace. -/
 @[protect_proj]
 structure AffineBasis (ι : Type u₁) (k : Type u₂) {V : Type u₃} (P : Type u₄) [AddCommGroup V]
-  [affine_space V P] [Ring k] [Module k V] where
+    [affine_space V P] [Ring k] [Module k V] where
   toFun : ι → P
   ind' : AffineIndependent k to_fun
   tot' : affineSpan k (range to_fun) = ⊤
@@ -245,7 +245,7 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
     (∑ i, b.Coord i v • b i) = v :=
   by
   have hb := b.affine_combination_coord_eq_self v
-  rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb
+  rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb 
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
 
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
@@ -321,7 +321,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
-    ∃ (s : _)(_ : s ⊆ t)(b : AffineBasis (↥s) k P), ⇑b = coe :=
+    ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = coe :=
   by
   obtain ⟨s, hst, h_tot, h_ind⟩ := exists_affineIndependent k V t
   refine' ⟨s, hst, ⟨coe, h_ind, _⟩, rfl⟩
@@ -330,7 +330,7 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
 
 variable (k V P)
 
-theorem exists_affineBasis : ∃ (s : Set P)(b : AffineBasis (↥s) k P), ⇑b = coe :=
+theorem exists_affineBasis : ∃ (s : Set P) (b : AffineBasis (↥s) k P), ⇑b = coe :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)
   ⟨s, hs⟩
 #align affine_basis.exists_affine_basis AffineBasis.exists_affineBasis

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

@@ -47,7 +47,7 @@ barycentric coordinate of `q : P` is `1 - fᵢ (q -ᵥ p i)`.
 -/
 
 
-open Affine BigOperators
+open scoped Affine BigOperators
 
 open Set
 

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

@@ -86,33 +86,15 @@ instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P
 #align affine_basis.fun_like AffineBasis.funLike
 -/
 
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 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=
   FunLike.coe_injective h
 #align affine_basis.ext AffineBasis.ext
 
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 theorem ind : AffineIndependent k b :=
   b.ind'
 #align affine_basis.ind AffineBasis.ind
 
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 theorem tot : affineSpan k (range b) = ⊤ :=
   b.tot'
 #align affine_basis.tot AffineBasis.tot
@@ -134,34 +116,16 @@ def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
 #align affine_basis.reindex AffineBasis.reindex
 -/
 
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 @[simp, norm_cast]
 theorem coe_reindex : ⇑(b.reindex e) = b ∘ e.symm :=
   rfl
 #align affine_basis.coe_reindex AffineBasis.coe_reindex
 
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 @[simp]
 theorem reindex_apply (i' : ι') : b.reindex e i' = b (e.symm i') :=
   rfl
 #align affine_basis.reindex_apply AffineBasis.reindex_apply
 
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 @[simp]
 theorem reindex_refl : b.reindex (Equiv.refl _) = b :=
   ext rfl
@@ -187,17 +151,11 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
 #align affine_basis.basis_of AffineBasis.basisOf
 -/
 
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 @[simp]
 theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b ↑j -ᵥ b i := by
   simp [basis_of]
 #align affine_basis.basis_of_apply AffineBasis.basisOf_apply
 
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 @[simp]
 theorem basisOf_reindex (i : ι') :
     (b.reindex e).basisOf i =
@@ -205,12 +163,6 @@ theorem basisOf_reindex (i : ι') :
   by ext j; simp
 #align affine_basis.basis_of_reindex AffineBasis.basisOf_reindex
 
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 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k
     where
@@ -221,23 +173,11 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k
       sub_add_eq_sub_sub_swap, add_comm, sub_eq_add_neg]
 #align affine_basis.coord AffineBasis.coord
 
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 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCoords :=
   rfl
 #align affine_basis.linear_eq_sum_coords AffineBasis.linear_eq_sumCoords
 
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 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   by
@@ -245,34 +185,22 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   classical simp [AffineBasis.coord]
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
 
-/- warning: affine_basis.coord_apply_eq -> AffineBasis.coord_apply_eq is a dubious translation:
-<too large>
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 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
   simp only [coord, Basis.coe_sumCoords, LinearEquiv.map_zero, LinearEquiv.coe_coe, sub_zero,
     AffineMap.coe_mk, Finsupp.sum_zero_index, vsub_self]
 #align affine_basis.coord_apply_eq AffineBasis.coord_apply_eq
 
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 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
   rw [coord, AffineMap.coe_mk, ← Subtype.coe_mk j h.symm, ← b.basis_of_apply,
     Basis.sumCoords_self_apply, sub_self]
 #align affine_basis.coord_apply_ne AffineBasis.coord_apply_ne
 
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 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
 #align affine_basis.coord_apply AffineBasis.coord_apply
 
-/- warning: affine_basis.coord_apply_combination_of_mem -> AffineBasis.coord_apply_combination_of_mem is a dubious translation:
-<too large>
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 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = w i := by
@@ -281,9 +209,6 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
       s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 
-/- warning: affine_basis.coord_apply_combination_of_not_mem -> AffineBasis.coord_apply_combination_of_not_mem is a dubious translation:
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 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = 0 := by
@@ -292,9 +217,6 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
       s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
-/- warning: affine_basis.sum_coord_apply_eq_one -> AffineBasis.sum_coord_apply_eq_one is a dubious translation:
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 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
   by
@@ -305,9 +227,6 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_one
 
-/- warning: affine_basis.affine_combination_coord_eq_self -> AffineBasis.affineCombination_coord_eq_self is a dubious translation:
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 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
     (Finset.univ.affineCombination k b fun i => b.Coord i q) = q :=
@@ -319,9 +238,6 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_self
 
-/- warning: affine_basis.linear_combination_coord_eq_self -> AffineBasis.linear_combination_coord_eq_self is a dubious translation:
-<too large>
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 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
 @[simp]
@@ -332,9 +248,6 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
   rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
 
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-<too large>
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 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
   cases nonempty_fintype ι
@@ -342,12 +255,6 @@ theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coor
   simp only [h]
 #align affine_basis.ext_elem AffineBasis.ext_elem
 
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 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
   by
@@ -364,12 +271,6 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_one
 
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 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
     intro x
@@ -383,12 +284,6 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
     simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 
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 /-- Barycentric coordinates as an affine map. -/
 noncomputable def coords : P →ᵃ[k] ι → k
     where
@@ -403,9 +298,6 @@ noncomputable def coords : P →ᵃ[k] ι → k
       AffineMap.map_vadd]
 #align affine_basis.coords AffineBasis.coords
 
-/- warning: affine_basis.coords_apply -> AffineBasis.coords_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
   rfl
@@ -419,9 +311,6 @@ variable [DivisionRing k] [Module k V]
 
 include V
 
-/- warning: affine_basis.coord_apply_centroid -> AffineBasis.coord_apply_centroid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroidₓ'. -/
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}
     (hi : i ∈ s) : b.Coord i (s.centroid k b) = (s.card : k)⁻¹ := by
@@ -430,9 +319,6 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
     Finset.centroidWeights]
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
-/- warning: affine_basis.exists_affine_subbasis -> AffineBasis.exists_affine_subbasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_basis.exists_affine_subbasis AffineBasis.exists_affine_subbasisₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _)(_ : s ⊆ t)(b : AffineBasis (↥s) k P), ⇑b = coe :=
@@ -444,9 +330,6 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
 
 variable (k V P)
 
-/- warning: affine_basis.exists_affine_basis -> AffineBasis.exists_affineBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_basis.exists_affine_basis AffineBasis.exists_affineBasisₓ'. -/
 theorem exists_affineBasis : ∃ (s : Set P)(b : AffineBasis (↥s) k P), ⇑b = coe :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)
   ⟨s, hs⟩

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

@@ -129,9 +129,7 @@ protected theorem nonempty : Nonempty ι :=
 #print AffineBasis.reindex /-
 /-- Composition of an affine basis and an equivalence of index types. -/
 def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
-  ⟨b ∘ e.symm, b.ind.comp_embedding e.symm.toEmbedding,
-    by
-    rw [e.symm.surjective.range_comp]
+  ⟨b ∘ e.symm, b.ind.comp_embedding e.symm.toEmbedding, by rw [e.symm.surjective.range_comp];
     exact b.3⟩
 #align affine_basis.reindex AffineBasis.reindex
 -/
@@ -179,10 +177,8 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
   Basis.mk ((affineIndependent_iff_linearIndependent_vsub k b i).mp b.ind)
     (by
       suffices
-        Submodule.span k (range fun j : { x // x ≠ i } => b ↑j -ᵥ b i) = vectorSpan k (range b)
-        by
-        rw [this, ← direction_affineSpan, b.tot, AffineSubspace.direction_top]
-        exact le_rfl
+        Submodule.span k (range fun j : { x // x ≠ i } => b ↑j -ᵥ b i) = vectorSpan k (range b) by
+        rw [this, ← direction_affineSpan, b.tot, AffineSubspace.direction_top]; exact le_rfl
       conv_rhs => rw [← image_univ]
       rw [vectorSpan_image_eq_span_vsub_set_right_ne k b (mem_univ i)]
       congr
@@ -206,9 +202,7 @@ Case conversion may be inaccurate. Consider using '#align affine_basis.basis_of_
 theorem basisOf_reindex (i : ι') :
     (b.reindex e).basisOf i =
       (b.basisOf <| e.symm i).reindex (e.subtypeEquiv fun _ => e.eq_symm_apply.Not) :=
-  by
-  ext j
-  simp
+  by ext j; simp
 #align affine_basis.basis_of_reindex AffineBasis.basisOf_reindex
 
 /- warning: affine_basis.coord -> AffineBasis.coord is a dubious translation:
@@ -304,9 +298,7 @@ Case conversion may be inaccurate. Consider using '#align affine_basis.sum_coord
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
   by
-  have hq : q ∈ affineSpan k (range b) := by
-    rw [b.tot]
-    exact AffineSubspace.mem_top k V q
+  have hq : q ∈ affineSpan k (range b) := by rw [b.tot]; exact AffineSubspace.mem_top k V q
   obtain ⟨w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan_of_fintype hq
   convert hw
   ext i
@@ -320,9 +312,7 @@ Case conversion may be inaccurate. Consider using '#align affine_basis.affine_co
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
     (Finset.univ.affineCombination k b fun i => b.Coord i q) = q :=
   by
-  have hq : q ∈ affineSpan k (range b) := by
-    rw [b.tot]
-    exact AffineSubspace.mem_top k V q
+  have hq : q ∈ affineSpan k (range b) := by rw [b.tot]; exact AffineSubspace.mem_top k V q
   obtain ⟨w, hw, rfl⟩ := eq_affineCombination_of_mem_affineSpan_of_fintype hq
   congr
   ext i
@@ -405,12 +395,8 @@ noncomputable def coords : P →ᵃ[k] ι → k
   toFun q i := b.Coord i q
   linear :=
     { toFun := fun v i => -(b.basisOf i).sumCoords v
-      map_add' := fun v w => by
-        ext i
-        simp only [LinearMap.map_add, Pi.add_apply, neg_add]
-      map_smul' := fun t v => by
-        ext i
-        simpa only [LinearMap.map_smul, Pi.smul_apply, smul_neg] }
+      map_add' := fun v w => by ext i; simp only [LinearMap.map_add, Pi.add_apply, neg_add]
+      map_smul' := fun t v => by ext i; simpa only [LinearMap.map_smul, Pi.smul_apply, smul_neg] }
   map_vadd' p v := by
     ext i
     simp only [linear_eq_sum_coords, LinearMap.coe_mk, LinearMap.neg_apply, Pi.vadd_apply',

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

@@ -192,10 +192,7 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
 -/
 
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 @[simp]
 theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b ↑j -ᵥ b i := by
@@ -203,10 +200,7 @@ theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b 
 #align affine_basis.basis_of_apply AffineBasis.basisOf_apply
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.basis_of_reindex AffineBasis.basisOf_reindexₓ'. -/
 @[simp]
 theorem basisOf_reindex (i : ι') :
@@ -258,10 +252,7 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
 
 /- warning: affine_basis.coord_apply_eq -> AffineBasis.coord_apply_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_eq AffineBasis.coord_apply_eqₓ'. -/
 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
@@ -270,10 +261,7 @@ theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
 #align affine_basis.coord_apply_eq AffineBasis.coord_apply_eq
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_ne AffineBasis.coord_apply_neₓ'. -/
 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
@@ -282,20 +270,14 @@ theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
 #align affine_basis.coord_apply_ne AffineBasis.coord_apply_ne
 
 /- warning: affine_basis.coord_apply -> AffineBasis.coord_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply AffineBasis.coord_applyₓ'. -/
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
 #align affine_basis.coord_apply AffineBasis.coord_apply
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -306,10 +288,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -320,10 +299,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
 /- warning: affine_basis.sum_coord_apply_eq_one -> AffineBasis.sum_coord_apply_eq_one is a dubious translation:
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 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
@@ -338,10 +314,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 #align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_one
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_selfₓ'. -/
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
@@ -357,10 +330,7 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
 #align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_self
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_selfₓ'. -/
 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
@@ -373,10 +343,7 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.ext_elem AffineBasis.ext_elemₓ'. -/
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
@@ -451,10 +418,7 @@ noncomputable def coords : P →ᵃ[k] ι → k
 #align affine_basis.coords AffineBasis.coords
 
 /- warning: affine_basis.coords_apply -> AffineBasis.coords_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
@@ -470,10 +434,7 @@ variable [DivisionRing k] [Module k V]
 include V
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroidₓ'. -/
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}
@@ -484,10 +445,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
 /- warning: affine_basis.exists_affine_subbasis -> AffineBasis.exists_affine_subbasis is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.exists_affine_subbasis AffineBasis.exists_affine_subbasisₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
@@ -501,10 +459,7 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
 variable (k V P)
 
 /- warning: affine_basis.exists_affine_basis -> AffineBasis.exists_affineBasis is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.exists_affine_basis AffineBasis.exists_affineBasisₓ'. -/
 theorem exists_affineBasis : ∃ (s : Set P)(b : AffineBasis (↥s) k P), ⇑b = coe :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)

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

@@ -140,7 +140,7 @@ def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u1}} {ι' : Type.{u5}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u4} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u1, u3, u2, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u5} ι ι'), Eq.{max (succ u5) (succ u4)} (forall (a : ι'), (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) a) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (AffineBasis.{u5, u3, u2, u4} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) _x) (AffineBasis.funLike.{u5, u3, u2, u4} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineBasis.reindex.{u1, u5, u3, u2, u4} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e)) (Function.comp.{succ u5, succ u1, succ u4} ι' ι P (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u3, u2, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u3, u2, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b) (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coe_reindex AffineBasis.coe_reindexₓ'. -/
 @[simp, norm_cast]
 theorem coe_reindex : ⇑(b.reindex e) = b ∘ e.symm :=
@@ -151,7 +151,7 @@ theorem coe_reindex : ⇑(b.reindex e) = b ∘ e.symm :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u5} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i' : ι'), Eq.{succ u5} P (coeFn.{max (succ u2) (succ u5), max (succ u2) (succ u5)} (AffineBasis.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι' -> P) (FunLike.hasCoeToFun.{max (succ u2) (succ u5), succ u2, succ u5} (AffineBasis.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) ι' (fun (_x : ι') => P) (AffineBasis.funLike.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4)) (AffineBasis.reindex.{u1, u2, u3, u4, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i') (coeFn.{max (succ u1) (succ u5), max (succ u1) (succ u5)} (AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u5), succ u1, succ u5} (AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i'))
 but is expected to have type
-  forall {ι : Type.{u1}} {ι' : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u5} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u4} ι ι') (i' : ι'), Eq.{succ u5} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) i') (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (AffineBasis.{u4, u3, u2, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) _x) (AffineBasis.funLike.{u4, u3, u2, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineBasis.reindex.{u1, u4, u3, u2, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i') (FunLike.coe.{max (succ u1) (succ u5), succ u1, succ u5} (AffineBasis.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b (FunLike.coe.{max (succ u1) (succ u4), succ u4, succ u1} (Equiv.{succ u4, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u4} ι ι' e) i'))
+  forall {ι : Type.{u1}} {ι' : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u5} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u4} ι ι') (i' : ι'), Eq.{succ u5} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) i') (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (AffineBasis.{u4, u3, u2, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι') => P) _x) (AffineBasis.funLike.{u4, u3, u2, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineBasis.reindex.{u1, u4, u3, u2, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i') (FunLike.coe.{max (succ u1) (succ u5), succ u1, succ u5} (AffineBasis.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u3, u2, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b (FunLike.coe.{max (succ u1) (succ u4), succ u4, succ u1} (Equiv.{succ u4, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u4, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u4} ι ι' e) i'))
 Case conversion may be inaccurate. Consider using '#align affine_basis.reindex_apply AffineBasis.reindex_applyₓ'. -/
 @[simp]
 theorem reindex_apply (i' : ι') : b.reindex e i' = b (e.symm i') :=
@@ -206,7 +206,7 @@ theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b 
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u5} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (succ u2) (succ u3) (succ u4)} (Basis.{u2, u3, u4} (Subtype.{succ u2} ι' (fun (j : ι') => Ne.{succ u2} ι' j i)) k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1) _inst_4) (AffineBasis.basisOf.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u3, u4, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (Basis.reindex.{u1, u2, u3, u4} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))) (Subtype.{succ u2} ι' (fun (j : ι') => Ne.{succ u2} ι' j i)) k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i)) (Equiv.subtypeEquiv.{succ u1, succ u2} ι ι' (fun (j : ι) => Ne.{succ u1} ι j (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i)) (fun (j : ι') => Ne.{succ u2} ι' j i) e (fun (_x : ι) => Iff.not (Eq.{succ u1} ι _x (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i)) (Eq.{succ u2} ι' (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e _x) i) (Equiv.eq_symm_apply.{succ u1, succ u2} ι ι' e i _x))))
 but is expected to have type
-  forall {ι : Type.{u1}} {ι' : Type.{u5}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u5} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (Basis.{u5, u4, u3} (Subtype.{succ u5} ι' (fun (j : ι') => Ne.{succ u5} ι' j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4) (AffineBasis.basisOf.{u5, u4, u3, u2} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u5, u4, u3, u2} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (Basis.reindex.{u1, u5, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i))) (Subtype.{succ u5} ι' (fun (j : ι') => Ne.{succ u5} ι' j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (Equiv.subtypeEquiv.{succ u1, succ u5} ι ι' (fun (j : ι) => Ne.{succ u1} ι j (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (fun (j : ι') => Ne.{succ u5} ι' j i) e (fun (_x : ι) => Iff.not (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) i) _x (FunLike.coe.{max (succ u5) (succ u1), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (Eq.{succ u5} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (FunLike.coe.{max (succ u5) (succ u1), succ u1, succ u5} (Equiv.{succ u1, succ u5} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u5} ι ι') e _x) i) (Equiv.eq_symm_apply.{succ u5, succ u1} ι ι' e i _x))))
+  forall {ι : Type.{u1}} {ι' : Type.{u5}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u5} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (Basis.{u5, u4, u3} (Subtype.{succ u5} ι' (fun (j : ι') => Ne.{succ u5} ι' j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4) (AffineBasis.basisOf.{u5, u4, u3, u2} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u5, u4, u3, u2} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (Basis.reindex.{u1, u5, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i))) (Subtype.{succ u5} ι' (fun (j : ι') => Ne.{succ u5} ι' j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (Equiv.subtypeEquiv.{succ u1, succ u5} ι ι' (fun (j : ι) => Ne.{succ u1} ι j (FunLike.coe.{max (succ u1) (succ u5), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (fun (j : ι') => Ne.{succ u5} ι' j i) e (fun (_x : ι) => Iff.not (Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) i) _x (FunLike.coe.{max (succ u5) (succ u1), succ u5, succ u1} (Equiv.{succ u5, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u5, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u5} ι ι' e) i)) (Eq.{succ u5} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (FunLike.coe.{max (succ u5) (succ u1), succ u1, succ u5} (Equiv.{succ u1, succ u5} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u1, succ u5} ι ι') e _x) i) (Equiv.eq_symm_apply.{succ u5, succ u1} ι ι' e i _x))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.basis_of_reindex AffineBasis.basisOf_reindexₓ'. -/
 @[simp]
 theorem basisOf_reindex (i : ι') :
@@ -248,7 +248,7 @@ theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCo
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u5} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (succ u4) (succ u5) (succ u3)} (AffineMap.{u3, u4, u5, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (AddCommGroupWithOne.toAddGroupWithOne.{u3} k (Ring.toAddCommGroupWithOne.{u3} k _inst_3))))) (AffineBasis.coord.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u3, u4, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 but is expected to have type
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (Semiring.toModule.{u5} k (Ring.toSemiring.{u5} k _inst_3)) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (Semiring.toModule.{u5} k (Ring.toSemiring.{u5} k _inst_3)) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_reindex AffineBasis.coord_reindexₓ'. -/
 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=

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

@@ -221,7 +221,7 @@ theorem basisOf_reindex (i : ι') :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3))))
+  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord AffineBasis.coordₓ'. -/
 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k
@@ -237,7 +237,7 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u3) (succ u2)} (LinearMap.{u2, u2, u3, u2} k k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (AffineMap.linear.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u3 u2} (LinearMap.{u2, u2, u3, u2} k k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (LinearMap.hasNeg.{u2, u2, u3, u2} k k V k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3)))) (Basis.sumCoords.{u1, u2, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u4) (succ u3)} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u4} k (Ring.toAddCommGroup.{u4} k _inst_3)) _inst_4 (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (AffineMap.linear.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u4 u3} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u4} k k V k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Ring.toAddCommGroup.{u4} k _inst_3) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) (Basis.sumCoords.{u1, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u4) (succ u3)} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u4} k (Ring.toAddCommGroup.{u4} k _inst_3)) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (AffineMap.linear.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u4 u3} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u4} k k V k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Ring.toAddCommGroup.{u4} k _inst_3) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) (Basis.sumCoords.{u1, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.linear_eq_sum_coords AffineBasis.linear_eq_sumCoordsₓ'. -/
 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCoords :=
@@ -248,7 +248,7 @@ theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCo
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u5} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (succ u4) (succ u5) (succ u3)} (AffineMap.{u3, u4, u5, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (AddCommGroupWithOne.toAddGroupWithOne.{u3} k (Ring.toAddCommGroupWithOne.{u3} k _inst_3))))) (AffineBasis.coord.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u3, u4, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 but is expected to have type
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u5} k _inst_3) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (Semiring.toModule.{u5} k (Ring.toSemiring.{u5} k _inst_3)) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_reindex AffineBasis.coord_reindexₓ'. -/
 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
@@ -261,7 +261,7 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b i)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Semiring.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toSemiring.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Semiring.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toSemiring.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_eq AffineBasis.coord_apply_eqₓ'. -/
 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
@@ -273,7 +273,7 @@ theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {i : ι} {j : ι}, (Ne.{succ u1} ι i j) -> (Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b j)) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3))))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_ne AffineBasis.coord_apply_neₓ'. -/
 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
@@ -285,7 +285,7 @@ theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u1} ι] (i : ι) (j : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b j)) (ite.{succ u2} k (Eq.{succ u1} ι i j) (_inst_5 i j) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))))))))
 but is expected to have type
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(Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (ite.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Eq.{succ u4} ι i j) (_inst_5 i j) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 1 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_inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3)))) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 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+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u4} ι] (i : ι) (j : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 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(AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply AffineBasis.coord_applyₓ'. -/
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
@@ -295,7 +295,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 lean 3 declaration is
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u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -309,7 +309,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 lean 3 declaration is
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 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Not (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s)) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -323,7 +323,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_oneₓ'. -/
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
@@ -341,7 +341,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u4} P (coeFn.{max (succ (max u1 u2)) (succ u3) (succ u4), max (succ (max u1 u2)) (succ u4)} (AffineMap.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k 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(Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
+  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_3)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_selfₓ'. -/
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
@@ -360,7 +360,7 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} [_inst_1 : AddCommGroup.{u3} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u3} V (Finset.sum.{u3, u1} V ι (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} k V (SMulZeroClass.toHasSmul.{u2, u3} k V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (SMulWithZero.toSmulZeroClass.{u2, u3} k V (MulZeroClass.toHasZero.{u2} k (MulZeroOneClass.toMulZeroClass.{u2} k (MonoidWithZero.toMulZeroOneClass.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (MulActionWithZero.toSMulWithZero.{u2, u3} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (Module.toMulActionWithZero.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4)))) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineMap.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => V -> k) (AffineMap.hasCoeToFun.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4 b i) v) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) => ι -> V) (FunLike.hasCoeToFun.{max (succ u1) (succ u3), succ u1, succ u3} (AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => V) (AffineBasis.funLike.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4)) b i))) v
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : AddCommGroup.{u1} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] [_inst_5 : Fintype.{u3} ι] (b : AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u1} V (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_1) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (instHSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SMulZeroClass.toSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (MonoidWithZero.toZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3))) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3)) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (Module.toMulActionWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3) (AddCommGroup.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) V (fun (_x : V) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) _x) (AffineMap.funLike.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4 b i) v) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) _x) (AffineBasis.funLike.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) b i))) v
+  forall {ι : Type.{u3}} {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : AddCommGroup.{u1} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] [_inst_5 : Fintype.{u3} ι] (b : AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u1} V (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_1) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (instHSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SMulZeroClass.toSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (MonoidWithZero.toZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) _inst_3))) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) _inst_3)) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (Module.toMulActionWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) v) _inst_3) (AddCommGroup.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) V (fun (_x : V) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : V) => k) _x) (AffineMap.funLike.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4 b i) v) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) _x) (AffineBasis.funLike.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) b i))) v
 Case conversion may be inaccurate. Consider using '#align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_selfₓ'. -/
 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
@@ -376,7 +376,7 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u1} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u4} P q₁ q₂)
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u4} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u1} P q₁ q₂)
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u4} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u1} P q₁ q₂)
 Case conversion may be inaccurate. Consider using '#align affine_basis.ext_elem AffineBasis.ext_elemₓ'. -/
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
@@ -389,7 +389,7 @@ theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coor
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u1} ι] (i : ι), Eq.{max (succ u4) (succ u2)} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (OfNat.mk.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (One.one.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Pi.instOne.{u4, u2} P (fun (ᾰ : P) => k) (fun (i : P) => AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (fun (i : P) => Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) _inst_3)))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) a) (fun (i : P) => Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) i) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) i) _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_oneₓ'. -/
 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
@@ -411,7 +411,7 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u1} ι] (i : ι), Function.Surjective.{succ u4, succ u2} P k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u4} ι] (i : ι), Function.Surjective.{succ u3, succ u2} P k (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, succ u2} (AffineMap.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
+  forall {ι : Type.{u4}} {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u4} ι] (i : ι), Function.Surjective.{succ u3, succ u2} P k (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, succ u2} (AffineMap.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.surjective_coord AffineBasis.surjective_coordₓ'. -/
 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
@@ -430,7 +430,7 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_3)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_3 ι))
+  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_3)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_3 ι))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords AffineBasis.coordsₓ'. -/
 /-- Barycentric coordinates as an affine map. -/
 noncomputable def coords : P →ᵃ[k] ι → k
@@ -454,7 +454,7 @@ noncomputable def coords : P →ᵃ[k] ι → k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ (max u1 u2)), max (succ u4) (succ (max u1 u2))} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) => P -> ι -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
@@ -473,7 +473,7 @@ include V
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : DivisionRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3))))] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) {s : Finset.{u1} ι} {i : ι}, (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4 b i) (Finset.centroid.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4)) b))) (Inv.inv.{u2} k (DivInvMonoid.toHasInv.{u2} k (DivisionRing.toDivInvMonoid.{u2} k _inst_3)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u2} Nat k (CoeTCₓ.coe.{1, succ u2} Nat k (Nat.castCoe.{u2} k (AddMonoidWithOne.toNatCast.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))))) (Finset.card.{u1} ι s))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k _inst_3))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k (DivisionRing.toRing.{u4} k _inst_3))) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroidₓ'. -/
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}

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

@@ -295,7 +295,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 lean 3 declaration is
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 but is expected to have type
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(AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -309,7 +309,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 lean 3 declaration is
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 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Not (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s)) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max 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AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -341,7 +341,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u4} P (coeFn.{max (succ (max u1 u2)) (succ u3) (succ u4), max (succ (max u1 u2)) (succ u4)} (AffineMap.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k 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(Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
+  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_selfₓ'. -/
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
@@ -454,7 +454,7 @@ noncomputable def coords : P →ᵃ[k] ι → k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ (max u1 u2)), max (succ u4) (succ (max u1 u2))} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) => P -> ι -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=

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

@@ -261,7 +261,7 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b i)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (NonAssocRing.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toNonAssocRing.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Semiring.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toSemiring.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_eq AffineBasis.coord_apply_eqₓ'. -/
 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
@@ -285,7 +285,7 @@ theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u1} ι] (i : ι) (j : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b j)) (ite.{succ u2} k (Eq.{succ u1} ι i j) (_inst_5 i j) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))) (OfNat.ofNat.{u2} k 0 (OfNat.mk.{u2} k 0 (Zero.zero.{u2} k (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))))))))
 but is expected to have type
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k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3)))) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 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+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u4} ι] (i : ι) (j : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (ite.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Eq.{succ u4} ι i j) (_inst_5 i j) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P 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_inst_2 _inst_3 _inst_4) b j)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply AffineBasis.coord_applyₓ'. -/
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
@@ -295,7 +295,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 lean 3 declaration is
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 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max 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: ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, 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(AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max 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=> P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} 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(AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -309,7 +309,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u1} ι} {i : ι}, (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s)) -> (forall {w : ι -> k}, (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) s w) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))) -> (Eq.{succ u2} k (coeFn.{max (succ 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -323,7 +323,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_oneₓ'. -/
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
@@ -389,7 +389,7 @@ theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coor
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u1} ι] (i : ι), Eq.{max (succ u4) (succ u2)} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (OfNat.mk.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (One.one.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Pi.instOne.{u4, u2} P (fun (ᾰ : P) => k) (fun (i : P) => AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (fun (i : P) => NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) _inst_3)))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (fun (i : P) => Semiring.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_oneₓ'. -/
 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
@@ -473,7 +473,7 @@ include V
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : DivisionRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3))))] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) {s : Finset.{u1} ι} {i : ι}, (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4 b i) (Finset.centroid.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4)) b))) (Inv.inv.{u2} k (DivInvMonoid.toHasInv.{u2} k (DivisionRing.toDivInvMonoid.{u2} k _inst_3)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u2} Nat k (CoeTCₓ.coe.{1, succ u2} Nat k (Nat.castCoe.{u2} k (AddMonoidWithOne.toNatCast.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))))) (Finset.card.{u1} ι s))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (Semiring.toNatCast.{u4} k (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroidₓ'. -/
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}

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

@@ -295,7 +295,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u1} ι} {i : ι}, (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (forall {w : ι -> k}, (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) s w) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))) -> (Eq.{succ u2} k (coeFn.{max (succ u3) 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(NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) _inst_1 _inst_4 _inst_2) => (ι -> k) -> P) (AffineMap.hasCoeToFun.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b)) w)) (w i)))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (a : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) a) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (max (succ (max u4 u3)) (succ u2)) (succ u1), succ (max u4 u3), succ u1} (AffineMap.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -309,7 +309,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u1} ι} {i : ι}, (Not (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s)) -> (forall {w : ι -> k}, (Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) s w) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))) -> (Eq.{succ u2} k (coeFn.{max (succ 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -341,7 +341,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u4} P (coeFn.{max (succ (max u1 u2)) (succ u3) (succ u4), max (succ (max u1 u2)) (succ u4)} (AffineMap.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k 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(FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b)) (fun (i : ι) => coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
+  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_selfₓ'. -/
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
@@ -454,7 +454,7 @@ noncomputable def coords : P →ᵃ[k] ι → k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ (max u1 u2)), max (succ u4) (succ (max u1 u2))} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) => P -> ι -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.basis
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! 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.Basis
 /-!
 # Affine bases and barycentric coordinates
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Suppose `P` is an affine space modelled on the module `V` over the ring `k`, and `p : ι → P` is an
 affine-independent family of points spanning `P`. Given this data, each point `q : P` may be written
 uniquely as an affine combination: `q = w₀ p₀ + w₁ p₁ + ⋯` for some (finitely-supported) weights

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -218,7 +218,7 @@ theorem basisOf_reindex (i : ι') :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3))))
+  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> ι -> (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord AffineBasis.coordₓ'. -/
 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k
@@ -234,7 +234,7 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u3) (succ u2)} (LinearMap.{u2, u2, u3, u2} k k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (AffineMap.linear.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u3 u2} (LinearMap.{u2, u2, u3, u2} k k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (LinearMap.hasNeg.{u2, u2, u3, u2} k k V k (Ring.toSemiring.{u2} k _inst_3) (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) _inst_4 (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k _inst_3)))) (Basis.sumCoords.{u1, u2, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u4) (succ u3)} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u4} k (Ring.toAddCommGroup.{u4} k _inst_3)) _inst_4 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (AffineMap.linear.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u4 u3} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u4} k k V k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Ring.toAddCommGroup.{u4} k _inst_3) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) (Basis.sumCoords.{u1, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{max (succ u4) (succ u3)} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (AddCommGroup.toAddCommMonoid.{u4} k (Ring.toAddCommGroup.{u4} k _inst_3)) _inst_4 (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (AffineMap.linear.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Neg.neg.{max u4 u3} (LinearMap.{u4, u4, u3, u4} k k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3))) V k (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3))) (LinearMap.instNegLinearMapToAddCommMonoid.{u4, u4, u3, u4} k k V k (Ring.toSemiring.{u4} k _inst_3) (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Ring.toAddCommGroup.{u4} k _inst_3) _inst_4 (Semiring.toModule.{u4} k (Ring.toSemiring.{u4} k _inst_3)) (RingHom.id.{u4} k (Semiring.toNonAssocSemiring.{u4} k (Ring.toSemiring.{u4} k _inst_3)))) (Basis.sumCoords.{u1, u4, u3} (Subtype.{succ u1} ι (fun (j : ι) => Ne.{succ u1} ι j i)) k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4 (AffineBasis.basisOf.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.linear_eq_sum_coords AffineBasis.linear_eq_sumCoordsₓ'. -/
 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCoords :=
@@ -245,7 +245,7 @@ theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCo
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u3}} {V : Type.{u4}} {P : Type.{u5}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u5} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u4} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (succ u4) (succ u5) (succ u3)} (AffineMap.{u3, u4, u5, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_3)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (AddCommGroupWithOne.toAddGroupWithOne.{u3} k (Ring.toAddCommGroupWithOne.{u3} k _inst_3))))) (AffineBasis.coord.{u2, u3, u4, u5} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u3, u4, u5} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 but is expected to have type
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u5} k _inst_3) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {k : Type.{u5}} {V : Type.{u4}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u4} V] [_inst_2 : AddTorsor.{u4, u3} V P (AddCommGroup.toAddGroup.{u4} V _inst_1)] [_inst_3 : Ring.{u5} k] [_inst_4 : Module.{u5, u4} k V (Ring.toSemiring.{u5} k _inst_3) (AddCommGroup.toAddCommMonoid.{u4} V _inst_1)] (b : AffineBasis.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (e : Equiv.{succ u1, succ u2} ι ι') (i : ι'), Eq.{max (max (succ u5) (succ u4)) (succ u3)} (AffineMap.{u5, u4, u3, u5, u5} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u5} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u5} k _inst_3) (addGroupIsAddTorsor.{u5} k (AddGroupWithOne.toAddGroup.{u5} k (Ring.toAddGroupWithOne.{u5} k _inst_3)))) (AffineBasis.coord.{u2, u5, u4, u3} ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineBasis.reindex.{u1, u2, u5, u4, u3} ι ι' k V P _inst_1 _inst_2 _inst_3 _inst_4 b e) i) (AffineBasis.coord.{u1, u5, u4, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e) i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_reindex AffineBasis.coord_reindexₓ'. -/
 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
@@ -258,7 +258,7 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4)) b i)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (NonAssocRing.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toNonAssocRing.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u1} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (i : ι), Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u1, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (OfNat.ofNat.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) 1 (One.toOfNat1.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (NonAssocRing.toOne.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) (Ring.toNonAssocRing.{u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineBasis.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b i)) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_eq AffineBasis.coord_apply_eqₓ'. -/
 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
@@ -270,7 +270,7 @@ theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {i : ι} {j : ι}, (Ne.{succ u4} ι i j) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_ne AffineBasis.coord_apply_neₓ'. -/
 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
@@ -282,7 +282,7 @@ theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
 lean 3 declaration is
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 but is expected to have type
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P) _x) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (ite.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Eq.{succ u4} ι i j) (_inst_5 i j) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 1 (One.toOfNat1.{u3} ((fun 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_inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) _inst_3)))) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) 0 (Zero.toOfNat0.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (MonoidWithZero.toZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Semiring.toMonoidWithZero.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (Ring.toSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} 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+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u4} ι] (i : ι) (j : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b j)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply AffineBasis.coord_applyₓ'. -/
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
@@ -292,7 +292,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 lean 3 declaration is
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ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u3, max u4 u3, max u4 u3, u2, u1} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u3} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u3} k _inst_3)) (Pi.module.{u4, u3, u3} ι (fun (i : ι) => k) k (Ring.toSemiring.{u3} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u3, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u3, u2, u1, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) w)) (w i)))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -306,7 +306,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 lean 3 declaration is
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: ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) 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 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {s : Finset.{u4} ι} {i : ι}, (Not (Membership.mem.{u4, u4} ι (Finset.{u4} ι) (Finset.instMembershipFinset.{u4} ι) i s)) -> (forall {w : ι -> k}, (Eq.{succ u3} k (Finset.sum.{u3, u4} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) s w) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))))) -> (Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (FunLike.coe.{max 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 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
@@ -320,7 +320,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u2} k (Finset.sum.{u2, u1} k ι (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u2} k 1 (OfNat.mk.{u2} k 1 (One.one.{u2} k (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Finset.sum.{u3, u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toNonUnitalNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3)))) (Finset.univ.{u4} ι _inst_5) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (OfNat.ofNat.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) 1 (One.toOfNat1.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_oneₓ'. -/
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
@@ -338,7 +338,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u1} ι] (q : P), Eq.{succ u4} P (coeFn.{max (succ (max u1 u2)) (succ u3) (succ u4), max (succ (max u1 u2)) (succ u4)} (AffineMap.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) _inst_1 _inst_4 _inst_2) (fun (_x : AffineMap.{u2, max u1 u2, max u1 u2, u3, u4} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k 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: ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u1} ι _inst_5) (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) => ι -> P) 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(Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
+  forall {ι : Type.{u4}} {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u1} k] [_inst_4 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Fintype.{u4} ι] (q : P), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) (FunLike.coe.{max (max (succ (max u4 u1)) (succ u2)) (succ u3), succ (max u4 u1), succ u3} (AffineMap.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (ι -> k) (fun (_x : ι -> k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : ι -> k) => P) _x) (AffineMap.funLike.{u1, max u4 u1, max u4 u1, u2, u3} k (ι -> k) (ι -> k) V P _inst_3 (Pi.addCommGroup.{u4, u1} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u1} k _inst_3)) (Pi.module.{u4, u1, u1} ι (fun (i : ι) => k) k (Ring.toSemiring.{u1} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u1, u4} k _inst_3 ι) _inst_1 _inst_4 _inst_2) (Finset.affineCombination.{u1, u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι (Finset.univ.{u4} ι _inst_5) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (AffineBasis.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (fun (i : ι) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (AffineMap.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u1, u2, u3, u1, u1} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u1} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} k _inst_3) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (Ring.toAddGroupWithOne.{u1} k _inst_3)))) (AffineBasis.coord.{u4, u1, u2, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)) q
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_selfₓ'. -/
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
@@ -357,7 +357,7 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} [_inst_1 : AddCommGroup.{u3} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u3} V (Finset.sum.{u3, u1} V ι (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) (Finset.univ.{u1} ι _inst_5) (fun (i : ι) => SMul.smul.{u2, u3} k V (SMulZeroClass.toHasSmul.{u2, u3} k V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (SMulWithZero.toSmulZeroClass.{u2, u3} k V (MulZeroClass.toHasZero.{u2} k (MulZeroOneClass.toMulZeroClass.{u2} k (MonoidWithZero.toMulZeroOneClass.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (MulActionWithZero.toSMulWithZero.{u2, u3} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)))) (Module.toMulActionWithZero.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1) _inst_4)))) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineMap.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => V -> k) (AffineMap.hasCoeToFun.{u2, u3, u3, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4 b i) v) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) => ι -> V) (FunLike.hasCoeToFun.{max (succ u1) (succ u3), succ u1, succ u3} (AffineBasis.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => V) (AffineBasis.funLike.{u1, u2, u3, u3} ι k V V _inst_1 (addGroupIsAddTorsor.{u3} V (AddCommGroup.toAddGroup.{u3} V _inst_1)) _inst_3 _inst_4)) b i))) v
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : AddCommGroup.{u1} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] [_inst_5 : Fintype.{u3} ι] (b : AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u1} V (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_1) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (instHSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SMulZeroClass.toSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (MonoidWithZero.toZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3))) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3)) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (Module.toMulActionWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3) (AddCommGroup.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) V (fun (_x : V) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) _x) (AffineMap.funLike.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4 b i) v) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) _x) (AffineBasis.funLike.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) b i))) v
+  forall {ι : Type.{u3}} {k : Type.{u2}} {V : Type.{u1}} [_inst_1 : AddCommGroup.{u1} V] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] [_inst_5 : Fintype.{u3} ι] (b : AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) (v : V), Eq.{succ u1} V (Finset.sum.{u1, u3} V ι (AddCommGroup.toAddCommMonoid.{u1} V _inst_1) (Finset.univ.{u3} ι _inst_5) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (instHSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SMulZeroClass.toSMul.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (SMulWithZero.toSMulZeroClass.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (MonoidWithZero.toZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3))) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (MulActionWithZero.toSMulWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Semiring.toMonoidWithZero.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3)) (NegZeroClass.toZero.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1))))) (Module.toMulActionWithZero.{u2, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) (Ring.toSemiring.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) v) _inst_3) (AddCommGroup.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) i) _inst_1) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) V (fun (_x : V) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : V) => k) _x) (AffineMap.funLike.{u2, u1, u1, u2, u2} k V V k k _inst_3 _inst_1 _inst_4 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4 b i) v) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => V) _x) (AffineBasis.funLike.{u3, u2, u1, u1} ι k V V _inst_1 (addGroupIsAddTorsor.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_1)) _inst_3 _inst_4) b i))) v
 Case conversion may be inaccurate. Consider using '#align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_selfₓ'. -/
 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
@@ -373,7 +373,7 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u1} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u4} P q₁ q₂)
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u4} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u1} P q₁ q₂)
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] (b : AffineBasis.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Finite.{succ u4} ι] {q₁ : P} {q₂ : P}, (forall (i : ι), Eq.{succ u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₁) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u1, succ u3} (AffineMap.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u2, u1, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u2, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q₂)) -> (Eq.{succ u1} P q₁ q₂)
 Case conversion may be inaccurate. Consider using '#align affine_basis.ext_elem AffineBasis.ext_elemₓ'. -/
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
@@ -386,7 +386,7 @@ theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coor
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u1} ι] (i : ι), Eq.{max (succ u4) (succ u2)} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (OfNat.mk.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) 1 (One.one.{max u4 u2} ((fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (Pi.instOne.{u4, u2} P (fun (ᾰ : P) => k) (fun (i : P) => AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (fun (i : P) => NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) _inst_3)))))
+  forall {ι : Type.{u4}} {k : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u2} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u3} k] [_inst_4 : Module.{u3, u1} k V (Ring.toSemiring.{u3} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Subsingleton.{succ u4} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, succ u3} (AffineMap.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u3, u1, u2, u3, u3} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u3} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_3) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_3)))) (AffineBasis.coord.{u4, u3, u1, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i)) (OfNat.ofNat.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) 1 (One.toOfNat1.{max u3 u2} (forall (a : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (Pi.instOne.{u2, u3} P (fun (a : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) a) (fun (i : P) => NonAssocRing.toOne.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) (Ring.toNonAssocRing.{u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) i) _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_oneₓ'. -/
 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
@@ -408,7 +408,7 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u1} ι] (i : ι), Function.Surjective.{succ u4, succ u2} P k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
 but is expected to have type
-  forall {ι : Type.{u4}} {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u4} ι] (i : ι), Function.Surjective.{succ u3, succ u2} P k (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, succ u2} (AffineMap.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
+  forall {ι : Type.{u4}} {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)] (b : AffineBasis.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nontrivial.{u4} ι] (i : ι), Function.Surjective.{succ u3, succ u2} P k (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, succ u2} (AffineMap.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u2, u1, u3, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u2} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_3)))) (AffineBasis.coord.{u4, u2, u1, u3} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.surjective_coord AffineBasis.surjective_coordₓ'. -/
 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
@@ -427,7 +427,7 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_3)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_3 ι))
+  forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)], (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) -> (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k _inst_3)) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k _inst_3 ι))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords AffineBasis.coordsₓ'. -/
 /-- Barycentric coordinates as an affine map. -/
 noncomputable def coords : P →ᵃ[k] ι → k
@@ -451,7 +451,7 @@ noncomputable def coords : P →ᵃ[k] ι → k
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ (max u1 u2)), max (succ u4) (succ (max u1 u2))} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) => P -> ι -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k _inst_3) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Pi.addTorsor.{u1, u2, u2} ι (fun (i : ι) => k) (fun (i : ι) => AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3)))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_3)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 but is expected to have type
-  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
+  forall {ι : Type.{u1}} {k : Type.{u4}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u2} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : Ring.{u4} k] [_inst_4 : Module.{u4, u3} k V (Ring.toSemiring.{u4} k _inst_3) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] (b : AffineBasis.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) (q : P) (i : ι), Eq.{succ u4} k (FunLike.coe.{max (max (succ u3) (succ u2)) (succ (max u1 u4)), succ u2, succ (max u1 u4)} (AffineMap.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u4, u3, u2, max u1 u4, max u1 u4} k V P (ι -> k) (ι -> k) _inst_3 _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u4} ι (fun (i : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u4} k _inst_3)) (Pi.module.{u1, u4, u4} ι (fun (i : ι) => k) k (Ring.toSemiring.{u4} k _inst_3) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} k (NonAssocRing.toNonUnitalNonAssocRing.{u4} k (Ring.toNonAssocRing.{u4} k _inst_3)))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3)) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u4, u1} k _inst_3 ι)) (AffineBasis.coords.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b) q i) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u4), succ u2, succ u4} (AffineMap.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u3, u2, u4, u4} k V P k k _inst_3 _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k _inst_3) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k _inst_3) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k _inst_3)))) (AffineBasis.coord.{u1, u4, u3, u2} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b i) q)
 Case conversion may be inaccurate. Consider using '#align affine_basis.coords_apply AffineBasis.coords_applyₓ'. -/
 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
@@ -470,7 +470,7 @@ include V
 lean 3 declaration is
   forall {ι : Type.{u1}} {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u4}} [_inst_1 : AddCommGroup.{u3} V] [_inst_2 : AddTorsor.{u3, u4} V P (AddCommGroup.toAddGroup.{u3} V _inst_1)] [_inst_3 : DivisionRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : CharZero.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3))))] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) {s : Finset.{u1} ι} {i : ι}, (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i s) -> (Eq.{succ u2} k (coeFn.{max (succ u3) (succ u4) (succ u2), max (succ u4) (succ u2)} (AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (fun (_x : AffineMap.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) => P -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, u2, u2} k V P k k (DivisionRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k _inst_3))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))) (AffineBasis.coord.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4 b i) (Finset.centroid.{u2, u3, u4, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) => ι -> P) (FunLike.hasCoeToFun.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => P) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4)) b))) (Inv.inv.{u2} k (DivInvMonoid.toHasInv.{u2} k (DivisionRing.toDivInvMonoid.{u2} k _inst_3)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat k (HasLiftT.mk.{1, succ u2} Nat k (CoeTCₓ.coe.{1, succ u2} Nat k (Nat.castCoe.{u2} k (AddMonoidWithOne.toNatCast.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k _inst_3)))))))) (Finset.card.{u1} ι s))))
 but is expected to have type
-  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
+  forall {ι : Type.{u3}} {k : Type.{u4}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : AddCommGroup.{u2} V] [_inst_2 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_1)] [_inst_3 : DivisionRing.{u4} k] [_inst_4 : Module.{u4, u2} k V (DivisionSemiring.toSemiring.{u4} k (DivisionRing.toDivisionSemiring.{u4} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_1)] [_inst_5 : CharZero.{u4} k (AddGroupWithOne.toAddMonoidWithOne.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3)))] (b : AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) {s : Finset.{u3} ι} {i : ι}, (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i s) -> (Eq.{succ u4} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (a : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) a) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u4), succ u1, succ u4} (AffineMap.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => k) _x) (AffineMap.funLike.{u4, u2, u1, u4, u4} k V P k k (DivisionRing.toRing.{u4} k _inst_3) _inst_1 _inst_4 _inst_2 (Ring.toAddCommGroup.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3)) (addGroupIsAddTorsor.{u4} k (AddGroupWithOne.toAddGroup.{u4} k (Ring.toAddGroupWithOne.{u4} k (DivisionRing.toRing.{u4} k _inst_3))))) (AffineBasis.coord.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4 b i) (Finset.centroid.{u4, u2, u1, u3} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι s (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (AffineBasis.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u3, u4, u2, u1} ι k V P _inst_1 _inst_2 (DivisionRing.toRing.{u4} k _inst_3) _inst_4) b))) (Inv.inv.{u4} k (DivisionRing.toInv.{u4} k _inst_3) (Nat.cast.{u4} k (NonAssocRing.toNatCast.{u4} k (Ring.toNonAssocRing.{u4} k (DivisionRing.toRing.{u4} k _inst_3))) (Finset.card.{u3} ι s))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroidₓ'. -/
 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

@@ -50,6 +50,7 @@ open Set
 
 universe u₁ u₂ u₃ u₄
 
+#print AffineBasis /-
 /-- An affine basis is a family of affine-independent points whose span is the top subspace. -/
 @[protect_proj]
 structure AffineBasis (ι : Type u₁) (k : Type u₂) {V : Type u₃} (P : Type u₄) [AddCommGroup V]
@@ -58,6 +59,7 @@ structure AffineBasis (ι : Type u₁) (k : Type u₂) {V : Type u₃} (P : Type
   ind' : AffineIndependent k to_fun
   tot' : affineSpan k (range to_fun) = ⊤
 #align affine_basis AffineBasis
+-/
 
 variable {ι ι' k V P : Type _} [AddCommGroup V] [affine_space V P]
 
@@ -73,32 +75,55 @@ instance : Inhabited (AffineBasis PUnit k PUnit) :=
 
 include V
 
+#print AffineBasis.funLike /-
 instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P
     where
   coe := AffineBasis.toFun
   coe_injective' f g h := by cases f <;> cases g <;> congr
 #align affine_basis.fun_like AffineBasis.funLike
+-/
 
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 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=
   FunLike.coe_injective h
 #align affine_basis.ext AffineBasis.ext
 
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 theorem ind : AffineIndependent k b :=
   b.ind'
 #align affine_basis.ind AffineBasis.ind
 
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 theorem tot : affineSpan k (range b) = ⊤ :=
   b.tot'
 #align affine_basis.tot AffineBasis.tot
 
 include b
 
+#print AffineBasis.nonempty /-
 protected theorem nonempty : Nonempty ι :=
   not_isEmpty_iff.mp fun hι => by
     simpa only [@range_eq_empty _ _ hι, AffineSubspace.span_empty, bot_ne_top] using b.tot
 #align affine_basis.nonempty AffineBasis.nonempty
+-/
 
+#print AffineBasis.reindex /-
 /-- Composition of an affine basis and an equivalence of index types. -/
 def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
   ⟨b ∘ e.symm, b.ind.comp_embedding e.symm.toEmbedding,
@@ -106,22 +131,42 @@ def reindex (e : ι ≃ ι') : AffineBasis ι' k P :=
     rw [e.symm.surjective.range_comp]
     exact b.3⟩
 #align affine_basis.reindex AffineBasis.reindex
+-/
 
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 @[simp, norm_cast]
 theorem coe_reindex : ⇑(b.reindex e) = b ∘ e.symm :=
   rfl
 #align affine_basis.coe_reindex AffineBasis.coe_reindex
 
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 @[simp]
 theorem reindex_apply (i' : ι') : b.reindex e i' = b (e.symm i') :=
   rfl
 #align affine_basis.reindex_apply AffineBasis.reindex_apply
 
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 @[simp]
 theorem reindex_refl : b.reindex (Equiv.refl _) = b :=
   ext rfl
 #align affine_basis.reindex_refl AffineBasis.reindex_refl
 
+#print AffineBasis.basisOf /-
 /-- Given an affine basis for an affine space `P`, if we single out one member of the family, we
 obtain a linear basis for the model space `V`.
 
@@ -141,12 +186,25 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
       ext v
       simp)
 #align affine_basis.basis_of AffineBasis.basisOf
+-/
 
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 @[simp]
 theorem basisOf_apply (i : ι) (j : { j : ι // j ≠ i }) : b.basisOf i j = b ↑j -ᵥ b i := by
   simp [basis_of]
 #align affine_basis.basis_of_apply AffineBasis.basisOf_apply
 
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 @[simp]
 theorem basisOf_reindex (i : ι') :
     (b.reindex e).basisOf i =
@@ -156,6 +214,12 @@ theorem basisOf_reindex (i : ι') :
   simp
 #align affine_basis.basis_of_reindex AffineBasis.basisOf_reindex
 
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 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k
     where
@@ -166,11 +230,23 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k
       sub_add_eq_sub_sub_swap, add_comm, sub_eq_add_neg]
 #align affine_basis.coord AffineBasis.coord
 
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 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.Coord i).linear = -(b.basisOf i).sumCoords :=
   rfl
 #align affine_basis.linear_eq_sum_coords AffineBasis.linear_eq_sumCoords
 
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 @[simp]
 theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   by
@@ -178,22 +254,46 @@ theorem coord_reindex (i : ι') : (b.reindex e).Coord i = b.Coord (e.symm i) :=
   classical simp [AffineBasis.coord]
 #align affine_basis.coord_reindex AffineBasis.coord_reindex
 
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 @[simp]
 theorem coord_apply_eq (i : ι) : b.Coord i (b i) = 1 := by
   simp only [coord, Basis.coe_sumCoords, LinearEquiv.map_zero, LinearEquiv.coe_coe, sub_zero,
     AffineMap.coe_mk, Finsupp.sum_zero_index, vsub_self]
 #align affine_basis.coord_apply_eq AffineBasis.coord_apply_eq
 
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 @[simp]
 theorem coord_apply_ne (h : i ≠ j) : b.Coord i (b j) = 0 := by
   rw [coord, AffineMap.coe_mk, ← Subtype.coe_mk j h.symm, ← b.basis_of_apply,
     Basis.sumCoords_self_apply, sub_self]
 #align affine_basis.coord_apply_ne AffineBasis.coord_apply_ne
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply AffineBasis.coord_applyₓ'. -/
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j then 1 else 0 := by
   cases eq_or_ne i j <;> simp [h]
 #align affine_basis.coord_apply AffineBasis.coord_apply
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = w i := by
@@ -202,6 +302,12 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
       s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_mem AffineBasis.coord_apply_combination_of_mem
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_memₓ'. -/
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
     b.Coord i (s.affineCombination k b w) = 0 := by
@@ -210,6 +316,12 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
       s.map_affine_combination b w hw]
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
+/- warning: affine_basis.sum_coord_apply_eq_one -> AffineBasis.sum_coord_apply_eq_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_oneₓ'. -/
 @[simp]
 theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :=
   by
@@ -222,6 +334,12 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.sum_coord_apply_eq_one AffineBasis.sum_coord_apply_eq_one
 
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 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
     (Finset.univ.affineCombination k b fun i => b.Coord i q) = q :=
@@ -235,6 +353,12 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
   exact b.coord_apply_combination_of_mem (Finset.mem_univ i) hw
 #align affine_basis.affine_combination_coord_eq_self AffineBasis.affineCombination_coord_eq_self
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_selfₓ'. -/
 /-- A variant of `affine_basis.affine_combination_coord_eq_self` for the special case when the
 affine space is a module so we can talk about linear combinations. -/
 @[simp]
@@ -245,6 +369,12 @@ theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (
   rwa [finset.univ.affine_combination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self
 
+/- warning: affine_basis.ext_elem -> AffineBasis.ext_elem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_basis.ext_elem AffineBasis.ext_elemₓ'. -/
 theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coord i q₂) : q₁ = q₂ :=
   by
   cases nonempty_fintype ι
@@ -252,6 +382,12 @@ theorem ext_elem [Finite ι] {q₁ q₂ : P} (h : ∀ i, b.Coord i q₁ = b.Coor
   simp only [h]
 #align affine_basis.ext_elem AffineBasis.ext_elem
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_oneₓ'. -/
 @[simp]
 theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i : P → k) = 1 :=
   by
@@ -268,6 +404,12 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_one
 
+/- warning: affine_basis.surjective_coord -> AffineBasis.surjective_coord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_basis.surjective_coord AffineBasis.surjective_coordₓ'. -/
 theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coord i := by
   classical
     intro x
@@ -281,6 +423,12 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
     simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 
+/- warning: affine_basis.coords -> AffineBasis.coords is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_basis.coords AffineBasis.coordsₓ'. -/
 /-- Barycentric coordinates as an affine map. -/
 noncomputable def coords : P →ᵃ[k] ι → k
     where
@@ -299,6 +447,12 @@ noncomputable def coords : P →ᵃ[k] ι → k
       AffineMap.map_vadd]
 #align affine_basis.coords AffineBasis.coords
 
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 @[simp]
 theorem coords_apply (q : P) (i : ι) : b.coords q i = b.Coord i q :=
   rfl
@@ -312,6 +466,12 @@ variable [DivisionRing k] [Module k V]
 
 include V
 
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 @[simp]
 theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset ι} {i : ι}
     (hi : i ∈ s) : b.Coord i (s.centroid k b) = (s.card : k)⁻¹ := by
@@ -320,6 +480,12 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
     Finset.centroidWeights]
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _)(_ : s ⊆ t)(b : AffineBasis (↥s) k P), ⇑b = coe :=
@@ -331,6 +497,12 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
 
 variable (k V P)
 
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+but is expected to have type
+  forall (k : Type.{u2}) (V : Type.{u1}) (P : Type.{u3}) [_inst_1 : AddCommGroup.{u1} V] [_inst_2 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_1)] [_inst_3 : DivisionRing.{u2} k] [_inst_4 : Module.{u2, u1} k V (DivisionSemiring.toSemiring.{u2} k (DivisionRing.toDivisionSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} V _inst_1)], Exists.{succ u3} (Set.{u3} P) (fun (s : Set.{u3} P) => Exists.{succ u3} (AffineBasis.{u3, u2, u1, u3} (Set.Elem.{u3} P s) k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) (fun (b : AffineBasis.{u3, u2, u1, u3} (Set.Elem.{u3} P s) k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) => Eq.{succ u3} (forall (a : Set.Elem.{u3} P s), (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : Set.Elem.{u3} P s) => P) a) (FunLike.coe.{succ u3, succ u3, succ u3} (AffineBasis.{u3, u2, u1, u3} (Set.Elem.{u3} P s) k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) (Set.Elem.{u3} P s) (fun (_x : Set.Elem.{u3} P s) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : Set.Elem.{u3} P s) => P) _x) (AffineBasis.funLike.{u3, u2, u1, u3} (Set.Elem.{u3} P s) k V P _inst_1 _inst_2 (DivisionRing.toRing.{u2} k _inst_3) _inst_4) b) (Subtype.val.{succ u3} P (fun (x : P) => Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) x s))))
+Case conversion may be inaccurate. Consider using '#align affine_basis.exists_affine_basis AffineBasis.exists_affineBasisₓ'. -/
 theorem exists_affineBasis : ∃ (s : Set P)(b : AffineBasis (↥s) k P), ⇑b = coe :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)
   ⟨s, hs⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.basis
-! leanprover-community/mathlib commit 2f4cdce0c2f2f3b8cd58f05d556d03b468e1eb2e
+! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -196,7 +196,7 @@ theorem coord_apply [DecidableEq ι] (i j : ι) : b.Coord i (b j) = if i = j the
 
 @[simp]
 theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination b w) = w i := by
+    b.Coord i (s.affineCombination k b w) = w i := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_true,
       mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq,
       s.map_affine_combination b w hw]
@@ -204,7 +204,7 @@ theorem coord_apply_combination_of_mem (hi : i ∈ s) {w : ι → k} (hw : s.Sum
 
 @[simp]
 theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s.Sum w = 1) :
-    b.Coord i (s.affineCombination b w) = 0 := by
+    b.Coord i (s.affineCombination k b w) = 0 := by
   classical simp only [coord_apply, hi, Finset.affineCombination_eq_linear_combination, if_false,
       mul_boole, hw, Function.comp_apply, smul_eq_mul, s.sum_ite_eq,
       s.map_affine_combination b w hw]
@@ -224,7 +224,7 @@ theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.Coord i q) = 1 :
 
 @[simp]
 theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
-    (Finset.univ.affineCombination b fun i => b.Coord i q) = q :=
+    (Finset.univ.affineCombination k b fun i => b.Coord i q) = q :=
   by
   have hq : q ∈ affineSpan k (range b) := by
     rw [b.tot]
@@ -264,7 +264,7 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.Coord i
   let s : Finset ι := {i}
   have hi : i ∈ s := by simp
   have hw : s.sum (Function.const ι (1 : k)) = 1 := by simp
-  have hq : q = s.affine_combination b (Function.const ι (1 : k)) := by simp
+  have hq : q = s.affine_combination k b (Function.const ι (1 : k)) := by simp
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_one
 
@@ -277,7 +277,7 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.Coo
     have hj : j ∈ s := by simp
     let w : ι → k := fun j' => if j' = i then x else 1 - x
     have hw : s.sum w = 1 := by simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
-    use s.affine_combination b w
+    use s.affine_combination k b w
     simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 

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

@@ -320,7 +320,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
     Finset.centroidWeights]
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (s «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (s «expr ⊆ » t) -/
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
     ∃ (s : _)(_ : s ⊆ t)(b : AffineBasis (↥s) k P), ⇑b = coe :=
   by

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

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

@@ -245,8 +245,8 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.coord i
     apply subsingleton_of_subsingleton
   haveI := AffineSubspace.subsingleton_of_subsingleton_span_eq_top hp b.tot
   let s : Finset ι := {i}
-  have hi : i ∈ s := by simp
-  have hw : s.sum (Function.const ι (1 : k)) = 1 := by simp
+  have hi : i ∈ s := by simp [s]
+  have hw : s.sum (Function.const ι (1 : k)) = 1 := by simp [s]
   have hq : q = s.affineCombination k b (Function.const ι (1 : k)) := by
     simp [eq_iff_true_of_subsingleton]
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw, Function.const_apply]
@@ -257,11 +257,11 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.coo
     intro x
     obtain ⟨j, hij⟩ := exists_ne i
     let s : Finset ι := {i, j}
-    have hi : i ∈ s := by simp
+    have hi : i ∈ s := by simp [s]
     let w : ι → k := fun j' => if j' = i then x else 1 - x
-    have hw : s.sum w = 1 := by simp [Finset.sum_ite, Finset.filter_insert, hij]
+    have hw : s.sum w = 1 := by simp [s, w, Finset.sum_ite, Finset.filter_insert, hij]
     use s.affineCombination k b w
-    simp [b.coord_apply_combination_of_mem hi hw]
+    simp [w, b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord
 
 /-- Barycentric coordinates as an affine map. -/

@@ -269,24 +269,9 @@ noncomputable def coords : P →ᵃ[k] ι → k where
   toFun q i := b.coord i q
   linear :=
     { toFun := fun v i => -(b.basisOf i).sumCoords v
-      map_add' := fun v w => by
-        ext i
-        simp only [LinearMap.map_add, Pi.add_apply, neg_add]
-      map_smul' := fun t v => by
-        ext i
-        simp only [LinearMap.map_smul, Pi.smul_apply, smul_neg, RingHom.id_apply, mul_neg] }
-  map_vadd' p v := by
-    ext i
-    -- Porting note:
-    -- mathlib3 proof was:
-    -- simp only [linear_eq_sumCoords, LinearMap.coe_mk, LinearMap.neg_apply, Pi.vadd_apply',
-    --   AffineMap.map_vadd]
-    -- but now we need to `dsimp` before `AffineMap.map_vadd` works.
-    rw [LinearMap.coe_mk, Pi.vadd_apply']
-    dsimp
-    rw [AffineMap.map_vadd, linear_eq_sumCoords,
-        LinearMap.neg_apply]
-    simp only [ne_eq, Basis.coe_sumCoords, vadd_eq_add]
+      map_add' := fun v w => by ext; simp only [LinearMap.map_add, Pi.add_apply, neg_add]
+      map_smul' := fun t v => by ext; simp }
+  map_vadd' p v := by ext; simp
 #align affine_basis.coords AffineBasis.coords
 
 @[simp]

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

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

@@ -67,10 +67,10 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i j : 
 instance : Inhabited (AffineBasis PUnit k PUnit) :=
   ⟨⟨id, affineIndependent_of_subsingleton k id, by simp⟩⟩
 
-instance instDFunLike : DFunLike (AffineBasis ι k P) ι fun _ => P where
+instance instFunLike : FunLike (AffineBasis ι k P) ι P where
   coe := AffineBasis.toFun
   coe_injective' f g h := by cases f; cases g; congr
-#align affine_basis.fun_like AffineBasis.instDFunLike
+#align affine_basis.fun_like AffineBasis.instFunLike
 
 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=

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

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

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

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

@@ -67,14 +67,14 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P) {s : Finset ι} {i j : 
 instance : Inhabited (AffineBasis PUnit k PUnit) :=
   ⟨⟨id, affineIndependent_of_subsingleton k id, by simp⟩⟩
 
-instance funLike : FunLike (AffineBasis ι k P) ι fun _ => P where
+instance instDFunLike : DFunLike (AffineBasis ι k P) ι fun _ => P where
   coe := AffineBasis.toFun
   coe_injective' f g h := by cases f; cases g; congr
-#align affine_basis.fun_like AffineBasis.funLike
+#align affine_basis.fun_like AffineBasis.instDFunLike
 
 @[ext]
 theorem ext {b₁ b₂ : AffineBasis ι k P} (h : (b₁ : ι → P) = b₂) : b₁ = b₂ :=
-  FunLike.coe_injective h
+  DFunLike.coe_injective h
 #align affine_basis.ext AffineBasis.ext
 
 theorem ind : AffineIndependent k b :=

This is a follow-up to #9215. It changes the following theorems and definitions:

• IsOpen.exists_subset_affineIndependent_span_eq_top
• IsConformalMap
• SimpleGraph.induce_connected_of_patches
• Submonoid.exists_list_of_mem_closure
• AddSubmonoid.exists_list_of_mem_closure
• AffineSubspace.mem_affineSpan_insert_iff
• AffineBasis.exists_affine_subbasis
• exists_affineIndependent
• LinearMap.mem_submoduleImage
• Basis.basis_singleton_iff
• atom_iff_nonzero_span
• finrank_eq_one_iff'
• Submodule.basis_of_pid_aux
• exists_linearIndependent_extension
• exists_linearIndependent
• countable_cover_nhdsWithin_of_sigma_compact
• mem_residual

Also deprecate ENNReal.exists_ne_top'.

@@ -309,7 +309,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
-    ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = ((↑) : s → P) := by
+    ∃ s ⊆ t, ∃ b : AffineBasis s k P, ⇑b = ((↑) : s → P) := by
   obtain ⟨s, hst, h_tot, h_ind⟩ := exists_affineIndependent k V t
   refine' ⟨s, hst, ⟨(↑), h_ind, _⟩, rfl⟩
   rw [Subtype.range_coe, h_tot, ht]

@@ -258,7 +258,6 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.coo
     obtain ⟨j, hij⟩ := exists_ne i
     let s : Finset ι := {i, j}
     have hi : i ∈ s := by simp
-    have _ : j ∈ s := by simp
     let w : ι → k := fun j' => if j' = i then x else 1 - x
     have hw : s.sum w = 1 := by simp [Finset.sum_ite, Finset.filter_insert, hij]
     use s.affineCombination k b w

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -180,7 +180,7 @@ theorem coord_apply_ne (h : i ≠ j) : b.coord i (b j) = 0 := by
 #align affine_basis.coord_apply_ne AffineBasis.coord_apply_ne
 
 theorem coord_apply [DecidableEq ι] (i j : ι) : b.coord i (b j) = if i = j then 1 else 0 := by
-  cases' eq_or_ne i j with h h <;> simp [h]
+  rcases eq_or_ne i j with h | h <;> simp [h]
 #align affine_basis.coord_apply AffineBasis.coord_apply
 
 @[simp]

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

@@ -247,7 +247,8 @@ theorem coe_coord_of_subsingleton_eq_one [Subsingleton ι] (i : ι) : (b.coord i
   let s : Finset ι := {i}
   have hi : i ∈ s := by simp
   have hw : s.sum (Function.const ι (1 : k)) = 1 := by simp
-  have hq : q = s.affineCombination k b (Function.const ι (1 : k)) := by simp
+  have hq : q = s.affineCombination k b (Function.const ι (1 : k)) := by
+    simp [eq_iff_true_of_subsingleton]
   rw [Pi.one_apply, hq, b.coord_apply_combination_of_mem hi hw, Function.const_apply]
 #align affine_basis.coe_coord_of_subsingleton_eq_one AffineBasis.coe_coord_of_subsingleton_eq_one
 

Match https://github.com/leanprover-community/mathlib/pull/18989

@@ -259,13 +259,7 @@ theorem surjective_coord [Nontrivial ι] (i : ι) : Function.Surjective <| b.coo
     have hi : i ∈ s := by simp
     have _ : j ∈ s := by simp
     let w : ι → k := fun j' => if j' = i then x else 1 - x
-    have hw : s.sum w = 1 := by
-      -- Porting note: previously this subgoal worked just by:
-      -- simp [hij, Finset.sum_ite, Finset.filter_insert, Finset.filter_eq']
-      -- I'm not sure why `simp` can not successfully use `Finset.filter_eq'`.
-      simp [Finset.sum_ite, Finset.filter_insert, hij]
-      erw [Finset.filter_eq']
-      simp [hij.symm]
+    have hw : s.sum w = 1 := by simp [Finset.sum_ite, Finset.filter_insert, hij]
     use s.affineCombination k b w
     simp [b.coord_apply_combination_of_mem hi hw]
 #align affine_basis.surjective_coord AffineBasis.surjective_coord

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

This has nice performance benefits.

@@ -55,7 +55,7 @@ structure AffineBasis (ι : Type u₁) (k : Type u₂) {V : Type u₃} (P : Type
   protected tot' : affineSpan k (range toFun) = ⊤
 #align affine_basis AffineBasis
 
-variable {ι ι' k V P : Type _} [AddCommGroup V] [AffineSpace V P]
+variable {ι ι' k V P : Type*} [AddCommGroup V] [AffineSpace V P]
 
 namespace AffineBasis
 

• 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 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.basis
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.AffineSpace.Independent
 import Mathlib.LinearAlgebra.Basis
 
+#align_import linear_algebra.affine_space.basis from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
+
 /-!
 # Affine bases and barycentric coordinates
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -203,7 +203,7 @@ theorem coord_apply_combination_of_not_mem (hi : i ∉ s) {w : ι → k} (hw : s
 #align affine_basis.coord_apply_combination_of_not_mem AffineBasis.coord_apply_combination_of_not_mem
 
 @[simp]
-theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : (∑ i, b.coord i q) = 1 := by
+theorem sum_coord_apply_eq_one [Fintype ι] (q : P) : ∑ i, b.coord i q = 1 := by
   have hq : q ∈ affineSpan k (range b) := by
     rw [b.tot]
     exact AffineSubspace.mem_top k V q
@@ -228,7 +228,7 @@ theorem affineCombination_coord_eq_self [Fintype ι] (q : P) :
 affine space is a module so we can talk about linear combinations. -/
 @[simp]
 theorem linear_combination_coord_eq_self [Fintype ι] (b : AffineBasis ι k V) (v : V) :
-    (∑ i, b.coord i v • b i) = v := by
+    ∑ i, b.coord i v • b i = v := by
   have hb := b.affineCombination_coord_eq_self v
   rwa [Finset.univ.affineCombination_eq_linear_combination _ _ (b.sum_coord_apply_eq_one v)] at hb
 #align affine_basis.linear_combination_coord_eq_self AffineBasis.linear_combination_coord_eq_self

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

@@ -318,7 +318,7 @@ theorem coord_apply_centroid [CharZero k] (b : AffineBasis ι k P) {s : Finset 
 #align affine_basis.coord_apply_centroid AffineBasis.coord_apply_centroid
 
 theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
-    ∃ (s : _)(_ : s ⊆ t)(b : AffineBasis (↥s) k P), ⇑b = ((↑) : s → P) := by
+    ∃ (s : _) (_ : s ⊆ t) (b : AffineBasis (↥s) k P), ⇑b = ((↑) : s → P) := by
   obtain ⟨s, hst, h_tot, h_ind⟩ := exists_affineIndependent k V t
   refine' ⟨s, hst, ⟨(↑), h_ind, _⟩, rfl⟩
   rw [Subtype.range_coe, h_tot, ht]
@@ -326,7 +326,7 @@ theorem exists_affine_subbasis {t : Set P} (ht : affineSpan k t = ⊤) :
 
 variable (k V P)
 
-theorem exists_affineBasis : ∃ (s : Set P)(b : AffineBasis (↥s) k P), ⇑b = ((↑) : s → P) :=
+theorem exists_affineBasis : ∃ (s : Set P) (b : AffineBasis (↥s) k P), ⇑b = ((↑) : s → P) :=
   let ⟨s, _, hs⟩ := exists_affine_subbasis (AffineSubspace.span_univ k V P)
   ⟨s, hs⟩
 #align affine_basis.exists_affine_basis AffineBasis.exists_affineBasis

These are all doc fixes

@@ -290,7 +290,7 @@ noncomputable def coords : P →ᵃ[k] ι → k where
     -- mathlib3 proof was:
     -- simp only [linear_eq_sumCoords, LinearMap.coe_mk, LinearMap.neg_apply, Pi.vadd_apply',
     --   AffineMap.map_vadd]
-    -- but now we need to `dsimp` before `AffinteMap.map_vadd` works.
+    -- but now we need to `dsimp` before `AffineMap.map_vadd` works.
     rw [LinearMap.coe_mk, Pi.vadd_apply']
     dsimp
     rw [AffineMap.map_vadd, linear_eq_sumCoords,

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>

@@ -146,7 +146,6 @@ theorem basisOf_reindex (i : ι') :
   simp
 #align affine_basis.basis_of_reindex AffineBasis.basisOf_reindex
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- The `i`th barycentric coordinate of a point. -/
 noncomputable def coord (i : ι) : P →ᵃ[k] k where
   toFun q := 1 - (b.basisOf i).sumCoords (q -ᵥ b i)
@@ -157,7 +156,6 @@ noncomputable def coord (i : ι) : P →ᵃ[k] k where
       sub_add_eq_sub_sub_swap, add_comm, sub_eq_add_neg]
 #align affine_basis.coord AffineBasis.coord
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 @[simp]
 theorem linear_eq_sumCoords (i : ι) : (b.coord i).linear = -(b.basisOf i).sumCoords :=
   rfl

This PR factors out a MetaM version of the rfl tactic and adds a missing whnfR and instantiateMVars in front of the goal type. This means that a few rws across mathlib4 now close the goal instead of e.g. requiring a trailing exact le_rfl.

Note: we do not use whnfR on the return type when adding the refl extension in the first place, as forallMetaTelescopeReducing already performs whnf (here, at reducible transparency).

See zulip for some discussion on the internal changes made.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -126,7 +126,6 @@ noncomputable def basisOf (i : ι) : Basis { j : ι // j ≠ i } k V :=
       suffices
         Submodule.span k (range fun j : { x // x ≠ i } => b ↑j -ᵥ b i) = vectorSpan k (range b) by
         rw [this, ← direction_affineSpan, b.tot, AffineSubspace.direction_top]
-        exact le_rfl
       conv_rhs => rw [← image_univ]
       rw [vectorSpan_image_eq_span_vsub_set_right_ne k b (mem_univ i)]
       congr

This PR fixes two things:

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

@@ -299,7 +299,6 @@ noncomputable def coords : P →ᵃ[k] ι → k where
     rw [AffineMap.map_vadd, linear_eq_sumCoords,
         LinearMap.neg_apply]
     simp only [ne_eq, Basis.coe_sumCoords, vadd_eq_add]
-
 #align affine_basis.coords AffineBasis.coords
 
 @[simp]

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