linear_algebra.affine_space.matrix ⟷ Mathlib.LinearAlgebra.AffineSpace.Matrix

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

@@ -163,7 +163,7 @@ theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
   by
   constructor
   · rintro ⟨⟨B, A, hA, hA'⟩, rfl : B = b.to_matrix p⟩
-    rw [Matrix.hMul_eq_hMul] at hA hA' 
+    rw [Matrix.hMul_eq_hMul] at hA hA'
     exact
       ⟨b.affine_independent_of_to_matrix_right_inv p hA,
         b.affine_span_eq_top_of_to_matrix_left_inv p hA'⟩
@@ -191,7 +191,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
     (b.toMatrix b₂)⁻¹.vecMul (b.coords x) = b₂.coords x :=
   by
   have hu := b.is_unit_to_matrix b₂
-  rw [Matrix.isUnit_iff_isUnit_det] at hu 
+  rw [Matrix.isUnit_iff_isUnit_det] at hu
   rw [← b.to_matrix_vec_mul_coords b₂, Matrix.vecMul_vecMul, Matrix.mul_nonsing_inv _ hu,
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
@@ -204,7 +204,7 @@ theorem det_smul_coords_eq_cramer_coords (x : P) :
     (b.toMatrix b₂).det • b₂.coords x = (b.toMatrix b₂)ᵀ.cramer (b.coords x) :=
   by
   have hu := b.is_unit_to_matrix b₂
-  rw [Matrix.isUnit_iff_isUnit_det] at hu 
+  rw [Matrix.isUnit_iff_isUnit_det] at hu
   rw [← b.to_matrix_inv_vec_mul_to_matrix, Matrix.det_smul_inv_vecMul_eq_cramer_transpose _ _ hu]
 #align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coords
 -/

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.Basis
-import Mathbin.LinearAlgebra.Determinant
+import LinearAlgebra.AffineSpace.Basis
+import LinearAlgebra.Determinant
 
 #align_import linear_algebra.affine_space.matrix from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
 

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

@@ -86,7 +86,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
       finset.univ.map_affine_combination p w₁ hw₁, ← finset.univ.map_affine_combination p w₂ hw₂,
       hweq]
   replace hweq' := congr_arg (fun w => A.vec_mul w) hweq'
-  simpa only [Matrix.vecMul_vecMul, ← Matrix.mul_eq_mul, hA, Matrix.vecMul_one] using hweq'
+  simpa only [Matrix.vecMul_vecMul, ← Matrix.hMul_eq_hMul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 -/
 
@@ -163,7 +163,7 @@ theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
   by
   constructor
   · rintro ⟨⟨B, A, hA, hA'⟩, rfl : B = b.to_matrix p⟩
-    rw [Matrix.mul_eq_mul] at hA hA' 
+    rw [Matrix.hMul_eq_hMul] at hA hA' 
     exact
       ⟨b.affine_independent_of_to_matrix_right_inv p hA,
         b.affine_span_eq_top_of_to_matrix_left_inv p hA'⟩

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.matrix
-! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.AffineSpace.Basis
 import Mathbin.LinearAlgebra.Determinant
 
+#align_import linear_algebra.affine_space.matrix from "leanprover-community/mathlib"@"fe8d0ff42c3c24d789f491dc2622b6cac3d61564"
+
 /-!
 # Matrix results for barycentric co-ordinates
 

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

@@ -59,7 +59,7 @@ theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   by
-  ext (i j)
+  ext i j
   rw [to_matrix_apply, coord_apply, Matrix.one_eq_pi_single, Pi.single_apply]
 #align affine_basis.to_matrix_self AffineBasis.toMatrix_self
 -/
@@ -145,7 +145,7 @@ variable [DecidableEq ι]
 #print AffineBasis.toMatrix_mul_toMatrix /-
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
-  ext (l m)
+  ext l m
   change (b₂.to_matrix b).vecMul (b.coords (b₂ l)) m = _
   rw [to_matrix_vec_mul_coords, coords_apply, ← to_matrix_apply, to_matrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix

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

@@ -47,25 +47,32 @@ noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k := f
 #align affine_basis.to_matrix AffineBasis.toMatrix
 -/
 
+#print AffineBasis.toMatrix_apply /-
 @[simp]
 theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
     b.toMatrix q i j = b.Coord j (q i) :=
   rfl
 #align affine_basis.to_matrix_apply AffineBasis.toMatrix_apply
+-/
 
+#print AffineBasis.toMatrix_self /-
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   by
   ext (i j)
   rw [to_matrix_apply, coord_apply, Matrix.one_eq_pi_single, Pi.single_apply]
 #align affine_basis.to_matrix_self AffineBasis.toMatrix_self
+-/
 
 variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
+#print AffineBasis.toMatrix_row_sum_one /-
 theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
+-/
 
+#print AffineBasis.affineIndependent_of_toMatrix_right_inv /-
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
 theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P) {A : Matrix ι ι' k}
@@ -84,7 +91,9 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
   replace hweq' := congr_arg (fun w => A.vec_mul w) hweq'
   simpa only [Matrix.vecMul_vecMul, ← Matrix.mul_eq_mul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
+-/
 
+#print AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv /-
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
 theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (p : ι' → P)
@@ -114,6 +123,7 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
   rw [hbi]
   exact affineCombination_mem_affineSpan hAi p
 #align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv
+-/
 
 #print AffineBasis.toMatrix_vecMul_coords /-
 /-- A change of basis formula for barycentric coordinates.
@@ -132,20 +142,25 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
 
 variable [DecidableEq ι]
 
+#print AffineBasis.toMatrix_mul_toMatrix /-
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
   ext (l m)
   change (b₂.to_matrix b).vecMul (b.coords (b₂ l)) m = _
   rw [to_matrix_vec_mul_coords, coords_apply, ← to_matrix_apply, to_matrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix
+-/
 
+#print AffineBasis.isUnit_toMatrix /-
 theorem isUnit_toMatrix : IsUnit (b.toMatrix b₂) :=
   ⟨{  val := b.toMatrix b₂
       inv := b₂.toMatrix b
       val_inv := b.toMatrix_mul_toMatrix b₂
       inv_val := b₂.toMatrix_mul_toMatrix b }, rfl⟩
 #align affine_basis.is_unit_to_matrix AffineBasis.isUnit_toMatrix
+-/
 
+#print AffineBasis.isUnit_toMatrix_iff /-
 theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
     IsUnit (b.toMatrix p) ↔ AffineIndependent k p ∧ affineSpan k (range p) = ⊤ :=
   by
@@ -160,6 +175,7 @@ theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
     change IsUnit (b.to_matrix b')
     exact b.is_unit_to_matrix b'
 #align affine_basis.is_unit_to_matrix_iff AffineBasis.isUnit_toMatrix_iff
+-/
 
 end Ring
 
@@ -169,6 +185,7 @@ variable [CommRing k] [Module k V] [DecidableEq ι] [Fintype ι]
 
 variable (b b₂ : AffineBasis ι k P)
 
+#print AffineBasis.toMatrix_inv_vecMul_toMatrix /-
 /-- A change of basis formula for barycentric coordinates.
 
 See also `affine_basis.to_matrix_vec_mul_coords`. -/
@@ -181,7 +198,9 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
   rw [← b.to_matrix_vec_mul_coords b₂, Matrix.vecMul_vecMul, Matrix.mul_nonsing_inv _ hu,
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
+-/
 
+#print AffineBasis.det_smul_coords_eq_cramer_coords /-
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/
 theorem det_smul_coords_eq_cramer_coords (x : P) :
@@ -191,6 +210,7 @@ theorem det_smul_coords_eq_cramer_coords (x : P) :
   rw [Matrix.isUnit_iff_isUnit_det] at hu 
   rw [← b.to_matrix_inv_vec_mul_to_matrix, Matrix.det_smul_inv_vecMul_eq_cramer_transpose _ _ hu]
 #align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coords
+-/
 
 end CommRing
 

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

@@ -62,7 +62,7 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
 
 variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
-theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j, b.toMatrix q i j) = 1 := by
+theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
@@ -76,7 +76,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
   have hweq' : (b.to_matrix p).vecMul w₁ = (b.to_matrix p).vecMul w₂ :=
     by
     ext j
-    change (∑ i, w₁ i • b.coord j (p i)) = ∑ i, w₂ i • b.coord j (p i)
+    change ∑ i, w₁ i • b.coord j (p i) = ∑ i, w₂ i • b.coord j (p i)
     rw [← finset.univ.affine_combination_eq_linear_combination _ _ hw₁, ←
       finset.univ.affine_combination_eq_linear_combination _ _ hw₂, ←
       finset.univ.map_affine_combination p w₁ hw₁, ← finset.univ.map_affine_combination p w₂ hw₂,
@@ -96,9 +96,9 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
     rintro q ⟨i, rfl⟩
     exact this i
   intro i
-  have hAi : (∑ j, A i j) = 1 := by
+  have hAi : ∑ j, A i j = 1 := by
     calc
-      (∑ j, A i j) = ∑ j, A i j * ∑ l, b.to_matrix p j l := by simp
+      ∑ j, A i j = ∑ j, A i j * ∑ l, b.to_matrix p j l := by simp
       _ = ∑ j, ∑ l, A i j * b.to_matrix p j l := by simp_rw [Finset.mul_sum]
       _ = ∑ l, ∑ j, A i j * b.to_matrix p j l := by rw [Finset.sum_comm]
       _ = ∑ l, (A ⬝ b.to_matrix p) i l := rfl

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

@@ -103,7 +103,6 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
       _ = ∑ l, ∑ j, A i j * b.to_matrix p j l := by rw [Finset.sum_comm]
       _ = ∑ l, (A ⬝ b.to_matrix p) i l := rfl
       _ = 1 := by simp [hA, Matrix.one_apply, Finset.filter_eq]
-      
   have hbi : b i = finset.univ.affine_combination k p (A i) :=
     by
     apply b.ext_elem

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

@@ -152,7 +152,7 @@ theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
   by
   constructor
   · rintro ⟨⟨B, A, hA, hA'⟩, rfl : B = b.to_matrix p⟩
-    rw [Matrix.mul_eq_mul] at hA hA'
+    rw [Matrix.mul_eq_mul] at hA hA' 
     exact
       ⟨b.affine_independent_of_to_matrix_right_inv p hA,
         b.affine_span_eq_top_of_to_matrix_left_inv p hA'⟩
@@ -178,7 +178,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
     (b.toMatrix b₂)⁻¹.vecMul (b.coords x) = b₂.coords x :=
   by
   have hu := b.is_unit_to_matrix b₂
-  rw [Matrix.isUnit_iff_isUnit_det] at hu
+  rw [Matrix.isUnit_iff_isUnit_det] at hu 
   rw [← b.to_matrix_vec_mul_coords b₂, Matrix.vecMul_vecMul, Matrix.mul_nonsing_inv _ hu,
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
@@ -189,7 +189,7 @@ theorem det_smul_coords_eq_cramer_coords (x : P) :
     (b.toMatrix b₂).det • b₂.coords x = (b.toMatrix b₂)ᵀ.cramer (b.coords x) :=
   by
   have hu := b.is_unit_to_matrix b₂
-  rw [Matrix.isUnit_iff_isUnit_det] at hu
+  rw [Matrix.isUnit_iff_isUnit_det] at hu 
   rw [← b.to_matrix_inv_vec_mul_to_matrix, Matrix.det_smul_inv_vecMul_eq_cramer_transpose _ _ hu]
 #align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coords
 

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

@@ -22,7 +22,7 @@ respect to some affine basis.
 -/
 
 
-open Affine BigOperators Matrix
+open scoped Affine BigOperators Matrix
 
 open Set
 

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

@@ -47,21 +47,12 @@ noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k := f
 #align affine_basis.to_matrix AffineBasis.toMatrix
 -/
 
-/- warning: affine_basis.to_matrix_apply -> AffineBasis.toMatrix_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_apply AffineBasis.toMatrix_applyₓ'. -/
 @[simp]
 theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
     b.toMatrix q i j = b.Coord j (q i) :=
   rfl
 #align affine_basis.to_matrix_apply AffineBasis.toMatrix_apply
 
-/- warning: affine_basis.to_matrix_self -> AffineBasis.toMatrix_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_self AffineBasis.toMatrix_selfₓ'. -/
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   by
@@ -71,19 +62,10 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
 
 variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
-/- warning: affine_basis.to_matrix_row_sum_one -> AffineBasis.toMatrix_row_sum_one is a dubious translation:
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 theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j, b.toMatrix q i j) = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
-/- warning: affine_basis.affine_independent_of_to_matrix_right_inv -> AffineBasis.affineIndependent_of_toMatrix_right_inv is a dubious translation:
-<too large>
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 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
 theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P) {A : Matrix ι ι' k}
@@ -103,9 +85,6 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
   simpa only [Matrix.vecMul_vecMul, ← Matrix.mul_eq_mul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 
-/- warning: affine_basis.affine_span_eq_top_of_to_matrix_left_inv -> AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv is a dubious translation:
-<too large>
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 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
 theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (p : ι' → P)
@@ -154,9 +133,6 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
 
 variable [DecidableEq ι]
 
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 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
   ext (l m)
@@ -164,12 +140,6 @@ theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   rw [to_matrix_vec_mul_coords, coords_apply, ← to_matrix_apply, to_matrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix
 
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 theorem isUnit_toMatrix : IsUnit (b.toMatrix b₂) :=
   ⟨{  val := b.toMatrix b₂
       inv := b₂.toMatrix b
@@ -177,12 +147,6 @@ theorem isUnit_toMatrix : IsUnit (b.toMatrix b₂) :=
       inv_val := b₂.toMatrix_mul_toMatrix b }, rfl⟩
 #align affine_basis.is_unit_to_matrix AffineBasis.isUnit_toMatrix
 
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 theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
     IsUnit (b.toMatrix p) ↔ AffineIndependent k p ∧ affineSpan k (range p) = ⊤ :=
   by
@@ -206,9 +170,6 @@ variable [CommRing k] [Module k V] [DecidableEq ι] [Fintype ι]
 
 variable (b b₂ : AffineBasis ι k P)
 
-/- warning: affine_basis.to_matrix_inv_vec_mul_to_matrix -> AffineBasis.toMatrix_inv_vecMul_toMatrix is a dubious translation:
-<too large>
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 /-- A change of basis formula for barycentric coordinates.
 
 See also `affine_basis.to_matrix_vec_mul_coords`. -/
@@ -222,9 +183,6 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
 
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-<too large>
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 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/
 theorem det_smul_coords_eq_cramer_coords (x : P) :

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

@@ -48,10 +48,7 @@ noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k := f
 -/
 
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 @[simp]
 theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
@@ -85,10 +82,7 @@ theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j,
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
 /- warning: affine_basis.affine_independent_of_to_matrix_right_inv -> AffineBasis.affineIndependent_of_toMatrix_right_inv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
@@ -110,10 +104,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 
 /- warning: affine_basis.affine_span_eq_top_of_to_matrix_left_inv -> AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
@@ -164,10 +155,7 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
 variable [DecidableEq ι]
 
 /- warning: affine_basis.to_matrix_mul_to_matrix -> AffineBasis.toMatrix_mul_toMatrix is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrixₓ'. -/
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
@@ -219,10 +207,7 @@ variable [CommRing k] [Module k V] [DecidableEq ι] [Fintype ι]
 variable (b b₂ : AffineBasis ι k P)
 
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 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
@@ -238,10 +223,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
 
 /- warning: affine_basis.det_smul_coords_eq_cramer_coords -> AffineBasis.det_smul_coords_eq_cramer_coords is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -241,7 +241,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 lean 3 declaration is
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(fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k 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 but is expected to have type
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ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -241,7 +241,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} 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 but is expected to have type
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+  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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) x) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} k ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) x) ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) x) (instHSMul.{u2, max u1 u2} k ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) x) (Pi.instSMul.{u1, u2, u2} ι k (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.2922 : ι) => k) (fun (i : ι) => Algebra.toSMul.{u2, u2} k k (CommRing.toCommSemiring.{u2} k _inst_3) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (Algebra.id.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} k k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (ι -> k) (ι -> k) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> k) => ι -> k) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} k k (ι -> k) (ι -> k) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -51,7 +51,7 @@ noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k := f
 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) {ι' : Type.{u5}} (q : ι' -> P) (i : ι') (j : ι), Eq.{succ u2} k (AffineBasis.toMatrix.{u1, u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q i j) (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 j) (q i))
 but is expected to have type
-  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} (q : ι' -> P) (i : ι') (j : ι), Eq.{succ u3} k (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q i j) (FunLike.coe.{max (max (succ u4) (succ u5)) (succ u3), succ u5, succ u3} (AffineMap.{u3, u4, u5, 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, u4, u5, 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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b j) (q i))
+  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} (q : ι' -> P) (i : ι') (j : ι), Eq.{succ u3} k (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q i j) (FunLike.coe.{max (max (succ u4) (succ u5)) (succ u3), succ u5, succ u3} (AffineMap.{u3, u4, u5, 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, u4, u5, 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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b j) (q i))
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_apply AffineBasis.toMatrix_applyₓ'. -/
 @[simp]
 theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
@@ -222,7 +222,7 @@ variable (b b₂ : AffineBasis ι k P)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasInv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) 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(Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
+  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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
@@ -241,7 +241,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3)))) (fun (ᾰ : ι) => k) (fun (i : ι) => addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k 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 but is expected to have type
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ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -222,7 +222,7 @@ variable (b b₂ : AffineBasis ι k P)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasInv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) 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(Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
+  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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max 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(a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
@@ -241,7 +241,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} 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(fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k 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 but is expected to have type
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ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => ι -> k) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} k k (ι -> k) (ι -> k) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3598 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -63,7 +63,7 @@ theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : 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)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u1} ι], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι k) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (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)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasOne.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_5 a b) (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))))) (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.{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], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} ι ι k) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.one.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_5 a b) (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{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)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : DecidableEq.{succ u1} ι], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} ι ι k) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.one.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_5 a b) (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_self AffineBasis.toMatrix_selfₓ'. -/
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
@@ -78,7 +78,7 @@ variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 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_6 : Fintype.{u1} ι] {ι' : Type.{u5}} (q : ι' -> P) (i : ι'), 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_6) (fun (j : ι) => AffineBasis.toMatrix.{u1, u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q 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)))))))
 but is expected to have type
-  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_6 : Fintype.{u2} ι] {ι' : Type.{u1}} (q : ι' -> P) (i : ι'), Eq.{succ u3} k (Finset.sum.{u3, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (Finset.univ.{u2} ι _inst_6) (fun (j : ι) => AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q i j)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))))
+  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_6 : Fintype.{u2} ι] {ι' : Type.{u1}} (q : ι' -> P) (i : ι'), Eq.{succ u3} k (Finset.sum.{u3, u2} k ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (Finset.univ.{u2} ι _inst_6) (fun (j : ι) => AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' q i j)) (OfNat.ofNat.{u3} k 1 (One.toOfNat1.{u3} k (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_oneₓ'. -/
 theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j, b.toMatrix q i j) = 1 := by
   simp
@@ -88,7 +88,7 @@ theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j,
 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) {ι' : Type.{u5}} [_inst_5 : Fintype.{u5} ι'] [_inst_6 : Fintype.{u1} ι] [_inst_7 : DecidableEq.{succ u5} ι'] (p : ι' -> P) {A : Matrix.{u1, u5, u2} ι ι' k}, (Eq.{succ (max u5 u2)} (Matrix.{u5, u5, u2} ι' ι' k) (Matrix.mul.{u2, u5, u1, u5} ι' ι ι' k _inst_6 (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (AffineBasis.toMatrix.{u1, u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p) A) (OfNat.ofNat.{max u5 u2} (Matrix.{u5, u5, u2} ι' ι' k) 1 (OfNat.mk.{max u5 u2} (Matrix.{u5, u5, u2} ι' ι' k) 1 (One.one.{max u5 u2} (Matrix.{u5, u5, u2} ι' ι' k) (Matrix.hasOne.{u2, u5} ι' k (fun (a : ι') (b : ι') => _inst_7 a b) (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))))) (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))))) -> (AffineIndependent.{u2, u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι' p)
 but is expected to have type
-  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} [_inst_5 : Fintype.{u1} ι'] [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u1} ι'] (p : ι' -> P) {A : Matrix.{u2, u1, u3} ι ι' k}, (Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} ι' ι' k) (Matrix.mul.{u3, u1, u2, u1} ι' ι ι' k _inst_6 (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p) A) (OfNat.ofNat.{max u3 u1} (Matrix.{u1, u1, u3} ι' ι' k) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u1, u1, u3} ι' ι' k) (Matrix.one.{u3, u1} ι' k (fun (a : ι') (b : ι') => _inst_7 a b) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_3))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))))) -> (AffineIndependent.{u3, u4, u5, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι' p)
+  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} [_inst_5 : Fintype.{u1} ι'] [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u1} ι'] (p : ι' -> P) {A : Matrix.{u2, u1, u3} ι ι' k}, (Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} ι' ι' k) (Matrix.mul.{u3, u1, u2, u1} ι' ι ι' k _inst_6 (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p) A) (OfNat.ofNat.{max u3 u1} (Matrix.{u1, u1, u3} ι' ι' k) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u1, u1, u3} ι' ι' k) (Matrix.one.{u3, u1} ι' k (fun (a : ι') (b : ι') => _inst_7 a b) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_3))) (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3)))))) -> (AffineIndependent.{u3, u4, u5, u1} k V P _inst_3 _inst_1 _inst_4 _inst_2 ι' p)
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
@@ -113,7 +113,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
 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) {ι' : Type.{u5}} [_inst_5 : Fintype.{u5} ι'] [_inst_6 : Fintype.{u1} ι] [_inst_7 : DecidableEq.{succ u1} ι] [_inst_8 : Nontrivial.{u2} k] (p : ι' -> P) {A : Matrix.{u1, u5, u2} ι ι' k}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι k) (Matrix.mul.{u2, u1, u5, u1} ι ι' ι k _inst_5 (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) A (AffineBasis.toMatrix.{u1, u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasOne.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))))) (AddMonoidWithOne.toOne.{u2} k (AddGroupWithOne.toAddMonoidWithOne.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k _inst_3))))))))) -> (Eq.{succ u4} (AffineSubspace.{u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2) (affineSpan.{u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2 (Set.range.{u4, succ u5} P ι' p)) (Top.top.{u4} (AffineSubspace.{u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2) (CompleteLattice.toHasTop.{u4} (AffineSubspace.{u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2) (AffineSubspace.completeLattice.{u2, u3, u4} k V P _inst_3 _inst_1 _inst_4 _inst_2))))
 but is expected to have type
-  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} [_inst_5 : Fintype.{u1} ι'] [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u2} ι] [_inst_8 : Nontrivial.{u3} k] (p : ι' -> P) {A : Matrix.{u2, u1, u3} ι ι' k}, (Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} ι ι k) (Matrix.mul.{u3, u2, u1, u2} ι ι' ι k _inst_5 (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) A (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p)) (OfNat.ofNat.{max u2 u3} (Matrix.{u2, u2, u3} ι ι k) 1 (One.toOfNat1.{max u2 u3} (Matrix.{u2, u2, u3} ι ι k) (Matrix.one.{u3, u2} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_3))) (NonAssocRing.toOne.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))))) -> (Eq.{succ u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (affineSpan.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2 (Set.range.{u5, succ u1} P ι' p)) (Top.top.{u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (CompleteLattice.toTop.{u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2))))
+  forall {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.{u2, u3, u4, u5} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) {ι' : Type.{u1}} [_inst_5 : Fintype.{u1} ι'] [_inst_6 : Fintype.{u2} ι] [_inst_7 : DecidableEq.{succ u2} ι] [_inst_8 : Nontrivial.{u3} k] (p : ι' -> P) {A : Matrix.{u2, u1, u3} ι ι' k}, (Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} ι ι k) (Matrix.mul.{u3, u2, u1, u2} ι ι' ι k _inst_5 (NonUnitalNonAssocRing.toMul.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} k (NonAssocRing.toNonUnitalNonAssocRing.{u3} k (Ring.toNonAssocRing.{u3} k _inst_3)))) A (AffineBasis.toMatrix.{u2, u3, u4, u5, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι' p)) (OfNat.ofNat.{max u2 u3} (Matrix.{u2, u2, u3} ι ι k) 1 (One.toOfNat1.{max u2 u3} (Matrix.{u2, u2, u3} ι ι k) (Matrix.one.{u3, u2} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MonoidWithZero.toZero.{u3} k (Semiring.toMonoidWithZero.{u3} k (Ring.toSemiring.{u3} k _inst_3))) (Semiring.toOne.{u3} k (Ring.toSemiring.{u3} k _inst_3)))))) -> (Eq.{succ u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (affineSpan.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2 (Set.range.{u5, succ u1} P ι' p)) (Top.top.{u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (CompleteLattice.toTop.{u5} (AffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u4, u5} k V P _inst_3 _inst_1 _inst_4 _inst_2))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
@@ -167,7 +167,7 @@ variable [DecidableEq 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)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_6 : Fintype.{u1} ι] (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_7 : DecidableEq.{succ u1} ι], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι k) (Matrix.mul.{u2, u1, u1, u1} ι ι ι k _inst_6 (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (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)) b₂)) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b₂ ι (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))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasOne.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MulZeroClass.toHasZero.{u2} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))))) (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.{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_6 : Fintype.{u1} ι] (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_7 : DecidableEq.{succ u1} ι], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} ι ι k) (Matrix.mul.{u2, u1, u1, u1} ι ι ι k _inst_6 (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b₂)) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b₂ ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.one.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{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)] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_6 : Fintype.{u1} ι] (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_7 : DecidableEq.{succ u1} ι], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} ι ι k) (Matrix.mul.{u2, u1, u1, u1} ι ι ι k _inst_6 (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k _inst_3)))) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b₂)) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 _inst_3 _inst_4 b₂ ι (FunLike.coe.{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) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 _inst_3 _inst_4) b))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.one.{u2, u1} ι k (fun (a : ι) (b : ι) => _inst_7 a b) (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_3))) (Semiring.toOne.{u2} k (Ring.toSemiring.{u2} k _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrixₓ'. -/
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
@@ -222,7 +222,7 @@ variable (b b₂ : AffineBasis ι k P)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (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 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(AddGroupWithOne.toAddGroup.{u2} k (AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.hasInv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) 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(Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
+  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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
@@ -241,7 +241,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} 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(AddCommGroupWithOne.toAddGroupWithOne.{u2} k (Ring.toAddCommGroupWithOne.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k 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 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (ι -> k) (fun (_x : ι -> k) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : ι -> k) => ι -> k) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} k k (ι -> k) (ι -> k) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : ι) => k) k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (CommSemiring.toSemiring.{u2} k (CommRing.toCommSemiring.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -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.matrix
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
+! leanprover-community/mathlib commit fe8d0ff42c3c24d789f491dc2622b6cac3d61564
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Determinant
 /-!
 # Matrix results for barycentric co-ordinates
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Results about the matrix of barycentric co-ordinates for a family of points in an affine space, with
 respect to some affine basis.
 -/

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

@@ -219,7 +219,7 @@ variable (b b₂ : AffineBasis ι k P)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (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 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=> P -> ι -> k) (AffineMap.hasCoeToFun.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
+  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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{max (succ u1) (succ u2)} (ι -> k) (Matrix.vecMul.{u2, u1, u1} ι ι k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))) _inst_6 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} ι ι k) (Matrix.inv.{u1, u2} ι k _inst_6 (fun (a : ι) (b : ι) => _inst_5 a b) _inst_3) (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)
 Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
@@ -238,7 +238,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} 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(Pi.addCommGroup.{u1, u2} ι (fun (i : ι) => k) (fun (i : ι) => NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b₂) x)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (ι -> k) (ι -> k) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.Function.module.{u1, u2, u2} ι k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Pi.Function.module.{u1, u2, u2} ι k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (ι -> k) (ι -> k) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3)))))) (Pi.Function.module.{u1, u2, u2} ι k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (Pi.Function.module.{u1, u2, u2} ι k k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3))))) => (ι -> k) -> ι -> k) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} k k (ι -> k) (ι -> k) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => k) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k 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(CommRing.toRing.{u2} k _inst_3))))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (RingHom.id.{u2} k (Semiring.toNonAssocSemiring.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (fun (_x : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.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 (CommRing.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 (CommRing.toRing.{u2} k _inst_3) _inst_4)) b₂)))) (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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (fun (_x : AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{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) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toAddCommGroup.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (CommRing.toRing.{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 (CommRing.toRing.{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 (CommRing.toRing.{u2} k _inst_3))))))) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
 but is expected to have type
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(Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)))) (RingHom.id.{u2} k (NonAssocRing.toNonAssocSemiring.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.cramer.{u1, u2} ι k (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 _inst_3 (Matrix.transpose.{u2, u1, u1} ι ι k (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b ι (FunLike.coe.{max (succ u1) (succ u4), succ u1, succ u4} (AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.AffineSpace.Basis._hyg.252 : ι) => P) _x) (AffineBasis.funLike.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) b₂)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ (max u1 u2)), succ u4, succ (max u1 u2)} (AffineMap.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} k _inst_3) _inst_1 _inst_4 _inst_2 (Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3599 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max 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 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -238,7 +238,7 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
 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 : CommRing.{u2} k] [_inst_4 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_1)] [_inst_5 : DecidableEq.{succ u1} ι] [_inst_6 : Fintype.{u1} ι] (b : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (b₂ : AffineBasis.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4) (x : P), Eq.{succ (max u1 u2)} (ι -> k) (SMul.smul.{u2, max u1 u2} k (ι -> k) (Function.hasSMul.{u1, u2, u2} ι k k (Mul.toSMul.{u2} k (Distrib.toHasMul.{u2} k (Ring.toDistrib.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (Matrix.det.{u2, u1} ι (fun (a : ι) (b : ι) => _inst_5 a b) _inst_6 k _inst_3 (AffineBasis.toMatrix.{u1, u2, u3, u4, u1} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/

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

@@ -35,19 +35,33 @@ section Ring
 
 variable [Ring k] [Module k V] (b : AffineBasis ι k P)
 
+#print AffineBasis.toMatrix /-
 /-- Given an affine basis `p`, and a family of points `q : ι' → P`, this is the matrix whose
 rows are the barycentric coordinates of `q` with respect to `p`.
 
 It is an affine equivalent of `basis.to_matrix`. -/
 noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k := fun i j => b.Coord j (q i)
 #align affine_basis.to_matrix AffineBasis.toMatrix
+-/
 
+/- warning: affine_basis.to_matrix_apply -> AffineBasis.toMatrix_apply is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
     b.toMatrix q i j = b.Coord j (q i) :=
   rfl
 #align affine_basis.to_matrix_apply AffineBasis.toMatrix_apply
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_self AffineBasis.toMatrix_selfₓ'. -/
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   by
@@ -57,10 +71,22 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
 
 variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
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 theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j, b.toMatrix q i j) = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
 theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P) {A : Matrix ι ι' k}
@@ -80,6 +106,12 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
   simpa only [Matrix.vecMul_vecMul, ← Matrix.mul_eq_mul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_invₓ'. -/
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
 theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (p : ι' → P)
@@ -111,6 +143,7 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
   exact affineCombination_mem_affineSpan hAi p
 #align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv
 
+#print AffineBasis.toMatrix_vecMul_coords /-
 /-- A change of basis formula for barycentric coordinates.
 
 See also `affine_basis.to_matrix_inv_mul_affine_basis_to_matrix`. -/
@@ -123,9 +156,16 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
   rw [Finset.map_affineCombination _ _ _ (b₂.sum_coord_apply_eq_one x)]
   simp [Matrix.vecMul, Matrix.dotProduct, to_matrix_apply, coords]
 #align affine_basis.to_matrix_vec_mul_coords AffineBasis.toMatrix_vecMul_coords
+-/
 
 variable [DecidableEq ι]
 
+/- warning: affine_basis.to_matrix_mul_to_matrix -> AffineBasis.toMatrix_mul_toMatrix is a dubious translation:
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 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   by
   ext (l m)
@@ -133,6 +173,12 @@ theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 :=
   rw [to_matrix_vec_mul_coords, coords_apply, ← to_matrix_apply, to_matrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix
 
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 theorem isUnit_toMatrix : IsUnit (b.toMatrix b₂) :=
   ⟨{  val := b.toMatrix b₂
       inv := b₂.toMatrix b
@@ -140,6 +186,12 @@ theorem isUnit_toMatrix : IsUnit (b.toMatrix b₂) :=
       inv_val := b₂.toMatrix_mul_toMatrix b }, rfl⟩
 #align affine_basis.is_unit_to_matrix AffineBasis.isUnit_toMatrix
 
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+Case conversion may be inaccurate. Consider using '#align affine_basis.is_unit_to_matrix_iff AffineBasis.isUnit_toMatrix_iffₓ'. -/
 theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
     IsUnit (b.toMatrix p) ↔ AffineIndependent k p ∧ affineSpan k (range p) = ⊤ :=
   by
@@ -163,6 +215,12 @@ variable [CommRing k] [Module k V] [DecidableEq ι] [Fintype ι]
 
 variable (b b₂ : AffineBasis ι k P)
 
+/- warning: affine_basis.to_matrix_inv_vec_mul_to_matrix -> AffineBasis.toMatrix_inv_vecMul_toMatrix is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrixₓ'. -/
 /-- A change of basis formula for barycentric coordinates.
 
 See also `affine_basis.to_matrix_vec_mul_coords`. -/
@@ -176,6 +234,12 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
 
+/- warning: affine_basis.det_smul_coords_eq_cramer_coords -> AffineBasis.det_smul_coords_eq_cramer_coords is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Pi.addCommGroup.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) (fun (i : ι) => Ring.toAddCommGroup.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.Combination._hyg.3609 : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P) => ι -> k) _x) (AffineMap.funLike.{u2, u3, u4, max u1 u2, max u1 u2} k V P (ι -> k) (ι -> k) (CommRing.toRing.{u2} 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 (CommRing.toRing.{u2} k _inst_3))) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => k) k (Ring.toSemiring.{u2} k (CommRing.toRing.{u2} k _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (CommRing.toRing.{u2} k _inst_3))))) (fun (i : ι) => AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (CommRing.toRing.{u2} k _inst_3))) (Finset.instAddTorsorForAllAddGroupToAddGroupToAddGroupWithOne.{u2, u1} k (CommRing.toRing.{u2} k _inst_3) ι)) (AffineBasis.coords.{u1, u2, u3, u4} ι k V P _inst_1 _inst_2 (CommRing.toRing.{u2} k _inst_3) _inst_4 b) x))
+Case conversion may be inaccurate. Consider using '#align affine_basis.det_smul_coords_eq_cramer_coords AffineBasis.det_smul_coords_eq_cramer_coordsₓ'. -/
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/
 theorem det_smul_coords_eq_cramer_coords (x : P) :

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.matrix
-! 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.
 -/
@@ -99,7 +99,7 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
       _ = ∑ l, (A ⬝ b.to_matrix p) i l := rfl
       _ = 1 := by simp [hA, Matrix.one_apply, Finset.filter_eq]
       
-  have hbi : b i = finset.univ.affine_combination p (A i) :=
+  have hbi : b i = finset.univ.affine_combination k p (A i) :=
     by
     apply b.ext_elem
     intro j

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

@@ -50,16 +50,17 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   rw [toMatrix_apply, coord_apply, Matrix.one_eq_pi_single, Pi.single_apply]
 #align affine_basis.to_matrix_self AffineBasis.toMatrix_self
 
-variable {ι' : Type*} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
+variable {ι' : Type*}
 
-theorem toMatrix_row_sum_one {ι' : Type*} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
+theorem toMatrix_row_sum_one [Fintype ι] (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
-theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P) {A : Matrix ι ι' k}
-    (hA : b.toMatrix p * A = 1) : AffineIndependent k p := by
+theorem affineIndependent_of_toMatrix_right_inv [Fintype ι] [Finite ι'] [DecidableEq ι']
+    (p : ι' → P) {A : Matrix ι ι' k} (hA : b.toMatrix p * A = 1) : AffineIndependent k p := by
+  cases nonempty_fintype ι'
   rw [affineIndependent_iff_eq_of_fintype_affineCombination_eq]
   intro w₁ w₂ hw₁ hw₂ hweq
   have hweq' : w₁ ᵥ* b.toMatrix p = w₂ ᵥ* b.toMatrix p := by
@@ -77,8 +78,10 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
 
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
-theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (p : ι' → P)
-    {A : Matrix ι ι' k} (hA : A * b.toMatrix p = 1) : affineSpan k (range p) = ⊤ := by
+theorem affineSpan_eq_top_of_toMatrix_left_inv [Finite ι] [Fintype ι'] [DecidableEq ι]
+    [Nontrivial k] (p : ι' → P) {A : Matrix ι ι' k} (hA : A * b.toMatrix p = 1) :
+    affineSpan k (range p) = ⊤ := by
+  cases nonempty_fintype ι
   suffices ∀ i, b i ∈ affineSpan k (range p) by
     rw [eq_top_iff, ← b.tot, affineSpan_le]
     rintro q ⟨i, rfl⟩
@@ -102,6 +105,8 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
   exact affineCombination_mem_affineSpan hAi p
 #align affine_basis.affine_span_eq_top_of_to_matrix_left_inv AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv
 
+variable [Fintype ι] (b₂ : AffineBasis ι k P)
+
 /-- A change of basis formula for barycentric coordinates.
 
 See also `AffineBasis.toMatrix_inv_vecMul_toMatrix`. -/

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -23,7 +23,6 @@ open Set
 universe u₁ u₂ u₃ u₄
 
 variable {ι : Type u₁} {k : Type u₂} {V : Type u₃} {P : Type u₄}
-
 variable [AddCommGroup V] [AffineSpace V P]
 
 namespace AffineBasis
@@ -147,7 +146,6 @@ end Ring
 section CommRing
 
 variable [CommRing k] [Module k V] [DecidableEq ι] [Fintype ι]
-
 variable (b b₂ : AffineBasis ι k P)
 
 /-- A change of basis formula for barycentric coordinates.

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

@@ -63,7 +63,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
     (hA : b.toMatrix p * A = 1) : AffineIndependent k p := by
   rw [affineIndependent_iff_eq_of_fintype_affineCombination_eq]
   intro w₁ w₂ hw₁ hw₂ hweq
-  have hweq' : (b.toMatrix p).vecMul w₁ = (b.toMatrix p).vecMul w₂ := by
+  have hweq' : w₁ ᵥ* b.toMatrix p = w₂ ᵥ* b.toMatrix p := by
     ext j
     change (∑ i, w₁ i • b.coord j (p i)) = ∑ i, w₂ i • b.coord j (p i)
     -- Porting note: Added `u` because `∘` was causing trouble
@@ -72,7 +72,7 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
       ← Finset.univ.affineCombination_eq_linear_combination _ _ hw₂, u,
       ← Finset.univ.map_affineCombination p w₁ hw₁, ← Finset.univ.map_affineCombination p w₂ hw₂,
       hweq]
-  replace hweq' := congr_arg (fun w => A.vecMul w) hweq'
+  replace hweq' := congr_arg (fun w => w ᵥ* A) hweq'
   simpa only [Matrix.vecMul_vecMul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 
@@ -107,7 +107,7 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
 
 See also `AffineBasis.toMatrix_inv_vecMul_toMatrix`. -/
 @[simp]
-theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x) = b.coords x := by
+theorem toMatrix_vecMul_coords (x : P) : b₂.coords x ᵥ* b.toMatrix b₂ = b.coords x := by
   ext j
   change _ = b.coord j x
   conv_rhs => rw [← b₂.affineCombination_coord_eq_self x]
@@ -119,7 +119,7 @@ variable [DecidableEq ι]
 
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ * b₂.toMatrix b = 1 := by
   ext l m
-  change (b₂.toMatrix b).vecMul (b.coords (b₂ l)) m = _
+  change (b.coords (b₂ l) ᵥ* b₂.toMatrix b) m = _
   rw [toMatrix_vecMul_coords, coords_apply, ← toMatrix_apply, toMatrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix
 
@@ -155,7 +155,7 @@ variable (b b₂ : AffineBasis ι k P)
 See also `AffineBasis.toMatrix_vecMul_coords`. -/
 @[simp]
 theorem toMatrix_inv_vecMul_toMatrix (x : P) :
-    (b.toMatrix b₂)⁻¹.vecMul (b.coords x) = b₂.coords x := by
+    b.coords x ᵥ* (b.toMatrix b₂)⁻¹ = b₂.coords x := by
   have hu := b.isUnit_toMatrix b₂
   rw [Matrix.isUnit_iff_isUnit_det] at hu
   rw [← b.toMatrix_vecMul_coords b₂, Matrix.vecMul_vecMul, Matrix.mul_nonsing_inv _ hu,

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
 import Mathlib.LinearAlgebra.AffineSpace.Basis
-import Mathlib.LinearAlgebra.Determinant
+import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
 
 #align_import linear_algebra.affine_space.matrix from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
 

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -60,7 +60,7 @@ theorem toMatrix_row_sum_one {ι' : Type*} (q : ι' → P) (i : ι') : ∑ j, b.
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a right inverse, then `p` is affine independent. -/
 theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P) {A : Matrix ι ι' k}
-    (hA : b.toMatrix p ⬝ A = 1) : AffineIndependent k p := by
+    (hA : b.toMatrix p * A = 1) : AffineIndependent k p := by
   rw [affineIndependent_iff_eq_of_fintype_affineCombination_eq]
   intro w₁ w₂ hw₁ hw₂ hweq
   have hweq' : (b.toMatrix p).vecMul w₁ = (b.toMatrix p).vecMul w₂ := by
@@ -73,13 +73,13 @@ theorem affineIndependent_of_toMatrix_right_inv [DecidableEq ι'] (p : ι' → P
       ← Finset.univ.map_affineCombination p w₁ hw₁, ← Finset.univ.map_affineCombination p w₂ hw₂,
       hweq]
   replace hweq' := congr_arg (fun w => A.vecMul w) hweq'
-  simpa only [Matrix.vecMul_vecMul, ← Matrix.mul_eq_mul, hA, Matrix.vecMul_one] using hweq'
+  simpa only [Matrix.vecMul_vecMul, hA, Matrix.vecMul_one] using hweq'
 #align affine_basis.affine_independent_of_to_matrix_right_inv AffineBasis.affineIndependent_of_toMatrix_right_inv
 
 /-- Given a family of points `p : ι' → P` and an affine basis `b`, if the matrix whose rows are the
 coordinates of `p` with respect `b` has a left inverse, then `p` spans the entire space. -/
 theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (p : ι' → P)
-    {A : Matrix ι ι' k} (hA : A ⬝ b.toMatrix p = 1) : affineSpan k (range p) = ⊤ := by
+    {A : Matrix ι ι' k} (hA : A * b.toMatrix p = 1) : affineSpan k (range p) = ⊤ := by
   suffices ∀ i, b i ∈ affineSpan k (range p) by
     rw [eq_top_iff, ← b.tot, affineSpan_le]
     rintro q ⟨i, rfl⟩
@@ -90,14 +90,14 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
       ∑ j, A i j = ∑ j, A i j * ∑ l, b.toMatrix p j l := by simp
       _ = ∑ j, ∑ l, A i j * b.toMatrix p j l := by simp_rw [Finset.mul_sum]
       _ = ∑ l, ∑ j, A i j * b.toMatrix p j l := by rw [Finset.sum_comm]
-      _ = ∑ l, (A ⬝ b.toMatrix p) i l := rfl
+      _ = ∑ l, (A * b.toMatrix p) i l := rfl
       _ = 1 := by simp [hA, Matrix.one_apply, Finset.filter_eq]
   have hbi : b i = Finset.univ.affineCombination k p (A i) := by
     apply b.ext_elem
     intro j
     rw [b.coord_apply, Finset.univ.map_affineCombination _ _ hAi,
       Finset.univ.affineCombination_eq_linear_combination _ _ hAi]
-    change _ = (A ⬝ b.toMatrix p) i j
+    change _ = (A * b.toMatrix p) i j
     simp_rw [hA, Matrix.one_apply, @eq_comm _ i j]
   rw [hbi]
   exact affineCombination_mem_affineSpan hAi p
@@ -117,7 +117,7 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
 
 variable [DecidableEq ι]
 
-theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 := by
+theorem toMatrix_mul_toMatrix : b.toMatrix b₂ * b₂.toMatrix b = 1 := by
   ext l m
   change (b₂.toMatrix b).vecMul (b.coords (b₂ l)) m = _
   rw [toMatrix_vecMul_coords, coords_apply, ← toMatrix_apply, toMatrix_self]
@@ -134,7 +134,6 @@ theorem isUnit_toMatrix_iff [Nontrivial k] (p : ι → P) :
     IsUnit (b.toMatrix p) ↔ AffineIndependent k p ∧ affineSpan k (range p) = ⊤ := by
   constructor
   · rintro ⟨⟨B, A, hA, hA'⟩, rfl : B = b.toMatrix p⟩
-    rw [Matrix.mul_eq_mul] at hA hA'
     exact ⟨b.affineIndependent_of_toMatrix_right_inv p hA,
       b.affineSpan_eq_top_of_toMatrix_left_inv p hA'⟩
   · rintro ⟨h_tot, h_ind⟩

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

This has nice performance benefits.

@@ -36,12 +36,12 @@ variable [Ring k] [Module k V] (b : AffineBasis ι k P)
 rows are the barycentric coordinates of `q` with respect to `p`.
 
 It is an affine equivalent of `Basis.toMatrix`. -/
-noncomputable def toMatrix {ι' : Type _} (q : ι' → P) : Matrix ι' ι k :=
+noncomputable def toMatrix {ι' : Type*} (q : ι' → P) : Matrix ι' ι k :=
   fun i j => b.coord j (q i)
 #align affine_basis.to_matrix AffineBasis.toMatrix
 
 @[simp]
-theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
+theorem toMatrix_apply {ι' : Type*} (q : ι' → P) (i : ι') (j : ι) :
     b.toMatrix q i j = b.coord j (q i) := rfl
 #align affine_basis.to_matrix_apply AffineBasis.toMatrix_apply
 
@@ -51,9 +51,9 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
   rw [toMatrix_apply, coord_apply, Matrix.one_eq_pi_single, Pi.single_apply]
 #align affine_basis.to_matrix_self AffineBasis.toMatrix_self
 
-variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
+variable {ι' : Type*} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
-theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
+theorem toMatrix_row_sum_one {ι' : Type*} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 

• 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.matrix
-! 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.Basis
 import Mathlib.LinearAlgebra.Determinant
 
+#align_import linear_algebra.affine_space.matrix from "leanprover-community/mathlib"@"2de9c37fa71dde2f1c6feff19876dd6a7b1519f0"
+
 /-!
 # Matrix results for barycentric co-ordinates
 

• 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

@@ -56,7 +56,7 @@ theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) :=
 
 variable {ι' : Type _} [Fintype ι'] [Fintype ι] (b₂ : AffineBasis ι k P)
 
-theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : (∑ j, b.toMatrix q i j) = 1 := by
+theorem toMatrix_row_sum_one {ι' : Type _} (q : ι' → P) (i : ι') : ∑ j, b.toMatrix q i j = 1 := by
   simp
 #align affine_basis.to_matrix_row_sum_one AffineBasis.toMatrix_row_sum_one
 
@@ -88,9 +88,9 @@ theorem affineSpan_eq_top_of_toMatrix_left_inv [DecidableEq ι] [Nontrivial k] (
     rintro q ⟨i, rfl⟩
     exact this i
   intro i
-  have hAi : (∑ j, A i j) = 1 := by
+  have hAi : ∑ j, A i j = 1 := by
     calc
-      (∑ j, A i j) = ∑ j, A i j * ∑ l, b.toMatrix p j l := by simp
+      ∑ j, A i j = ∑ j, A i j * ∑ l, b.toMatrix p j l := by simp
       _ = ∑ j, ∑ l, A i j * b.toMatrix p j l := by simp_rw [Finset.mul_sum]
       _ = ∑ l, ∑ j, A i j * b.toMatrix p j l := by rw [Finset.sum_comm]
       _ = ∑ l, (A ⬝ b.toMatrix p) i l := rfl

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

@@ -50,7 +50,7 @@ theorem toMatrix_apply {ι' : Type _} (q : ι' → P) (i : ι') (j : ι) :
 
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : b.toMatrix b = (1 : Matrix ι ι k) := by
-  ext (i j)
+  ext i j
   rw [toMatrix_apply, coord_apply, Matrix.one_eq_pi_single, Pi.single_apply]
 #align affine_basis.to_matrix_self AffineBasis.toMatrix_self
 
@@ -121,7 +121,7 @@ theorem toMatrix_vecMul_coords (x : P) : (b.toMatrix b₂).vecMul (b₂.coords x
 variable [DecidableEq ι]
 
 theorem toMatrix_mul_toMatrix : b.toMatrix b₂ ⬝ b₂.toMatrix b = 1 := by
-  ext (l m)
+  ext l m
   change (b₂.toMatrix b).vecMul (b.coords (b₂ l)) m = _
   rw [toMatrix_vecMul_coords, coords_apply, ← toMatrix_apply, toMatrix_self]
 #align affine_basis.to_matrix_mul_to_matrix AffineBasis.toMatrix_mul_toMatrix

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>

@@ -166,7 +166,6 @@ theorem toMatrix_inv_vecMul_toMatrix (x : P) :
     Matrix.vecMul_one]
 #align affine_basis.to_matrix_inv_vec_mul_to_matrix AffineBasis.toMatrix_inv_vecMul_toMatrix
 
-set_option synthInstance.etaExperiment true in
 /-- If we fix a background affine basis `b`, then for any other basis `b₂`, we can characterise
 the barycentric coordinates provided by `b₂` in terms of determinants relative to `b`. -/
 theorem det_smul_coords_eq_cramer_coords (x : P) :