linear_algebra.matrix.charpoly.linear_map

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

62c0a4ef

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4280f5f3

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -133,7 +133,7 @@ theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
   constructor
   · intro h i
     have := LinearMap.congr_fun h (Pi.single i 1)
-    rwa [PiToModule.fromEnd_apply_single_one, PiToModule.fromMatrix_apply_single_one] at this 
+    rwa [PiToModule.fromEnd_apply_single_one, PiToModule.fromMatrix_apply_single_one] at this
   · intro h
     ext
     simp_rw [LinearMap.comp_apply, LinearMap.coe_single, PiToModule.fromEnd_apply_single_one,
@@ -250,7 +250,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
     dsimp [A]
     intro j
     specialize hbM' (b j)
-    rwa [Ideal.finsuppTotal_apply_eq_of_fintype] at hbM' 
+    rwa [Ideal.finsuppTotal_apply_eq_of_fintype] at hbM'
   exact
     ⟨⟨A, f, this⟩, Matrix.isRepresentation.eq_toEnd_of_represents R b hb ⟨A, f, this⟩ this,
       fun i j => (bM' (b j) i).Prop⟩

4280f5f3

bump to nightly-2024-02-17-08

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

42bef5c2

Diff

@@ -290,7 +290,7 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
       (by rw [Subtype.range_coe_subtype, Finset.setOf_mem, hs]) f I hI
   refine' ⟨A.1.charpoly, A.1.charpoly_monic, _, _⟩
   · rw [A.1.charpoly_natDegree_eq_dim]
-    exact coeff_charpoly_mem_ideal_pow h
+    exact Matrix.coeff_charpoly_mem_ideal_pow h
   · rw [Polynomial.aeval_algHom_apply, ← map_zero (Matrix.isRepresentation.toEnd R coe _)]
     congr 1
     ext1

4280f5f3

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -282,6 +282,21 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
     [Module.Finite R M] (f : Module.End R M) (I : Ideal R) (hI : f.range ≤ I • ⊤) :
     ∃ p : R[X], p.Monic ∧ (∀ k, p.coeff k ∈ I ^ (p.natDegree - k)) ∧ Polynomial.aeval f p = 0 := by
   classical
+  cases subsingleton_or_nontrivial R
+  · exact ⟨0, Polynomial.monic_of_subsingleton _, by simp⟩
+  obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ := Module.Finite.out
+  obtain ⟨A, rfl, h⟩ :=
+    Matrix.isRepresentation.toEnd_exists_mem_ideal R (coe : s → M)
+      (by rw [Subtype.range_coe_subtype, Finset.setOf_mem, hs]) f I hI
+  refine' ⟨A.1.charpoly, A.1.charpoly_monic, _, _⟩
+  · rw [A.1.charpoly_natDegree_eq_dim]
+    exact coeff_charpoly_mem_ideal_pow h
+  · rw [Polynomial.aeval_algHom_apply, ← map_zero (Matrix.isRepresentation.toEnd R coe _)]
+    congr 1
+    ext1
+    rw [Polynomial.aeval_subalgebra_coe, Subtype.val_eq_coe, Matrix.aeval_self_charpoly,
+      Subalgebra.coe_zero]
+  · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
 -/

4280f5f3

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -282,21 +282,6 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
     [Module.Finite R M] (f : Module.End R M) (I : Ideal R) (hI : f.range ≤ I • ⊤) :
     ∃ p : R[X], p.Monic ∧ (∀ k, p.coeff k ∈ I ^ (p.natDegree - k)) ∧ Polynomial.aeval f p = 0 := by
   classical
-  cases subsingleton_or_nontrivial R
-  · exact ⟨0, Polynomial.monic_of_subsingleton _, by simp⟩
-  obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ := Module.Finite.out
-  obtain ⟨A, rfl, h⟩ :=
-    Matrix.isRepresentation.toEnd_exists_mem_ideal R (coe : s → M)
-      (by rw [Subtype.range_coe_subtype, Finset.setOf_mem, hs]) f I hI
-  refine' ⟨A.1.charpoly, A.1.charpoly_monic, _, _⟩
-  · rw [A.1.charpoly_natDegree_eq_dim]
-    exact coeff_charpoly_mem_ideal_pow h
-  · rw [Polynomial.aeval_algHom_apply, ← map_zero (Matrix.isRepresentation.toEnd R coe _)]
-    congr 1
-    ext1
-    rw [Polynomial.aeval_subalgebra_coe, Subtype.val_eq_coe, Matrix.aeval_self_charpoly,
-      Subalgebra.coe_zero]
-  · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
 -/

4280f5f3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.LinearAlgebra.Matrix.Charpoly.Coeff
-import Mathbin.LinearAlgebra.Matrix.ToLin
+import LinearAlgebra.Matrix.Charpoly.Coeff
+import LinearAlgebra.Matrix.ToLin
 
 #align_import linear_algebra.matrix.charpoly.linear_map from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"

4280f5f3

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -200,7 +200,7 @@ endomorphisms on `M`. -/
 def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
     where
   carrier := {A | ∃ f : Module.End R M, A.Represents b f}
-  mul_mem' := fun A₁ A₂ ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ * f₂, e₁.mul e₂⟩
+  hMul_mem' := fun A₁ A₂ ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ * f₂, e₁.mul e₂⟩
   one_mem' := ⟨1, Matrix.Represents.one⟩
   add_mem' := fun A₁ A₂ ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ + f₂, e₁.add e₂⟩
   zero_mem' := ⟨0, Matrix.Represents.zero⟩

4280f5f3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.linear_map
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Matrix.Charpoly.Coeff
 import Mathbin.LinearAlgebra.Matrix.ToLin
 
+#align_import linear_algebra.matrix.charpoly.linear_map from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 
 # Calyley-Hamilton theorem for f.g. modules.

4280f5f3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,17 +47,21 @@ def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R)
 #align pi_to_module.from_matrix PiToModule.fromMatrix
 -/
 
+#print PiToModule.fromMatrix_apply /-
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
     PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
   rfl
 #align pi_to_module.from_matrix_apply PiToModule.fromMatrix_apply
+-/
 
+#print PiToModule.fromMatrix_apply_single_one /-
 theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι ι R) (j : ι) :
     PiToModule.fromMatrix R b A (Pi.single j 1) = ∑ i : ι, A i j • b i :=
   by
   rw [PiToModule.fromMatrix_apply, Fintype.total_apply, Matrix.mulVec_single]
   simp_rw [mul_one]
 #align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_one
+-/
 
 #print PiToModule.fromEnd /-
 /-- The endomorphisms of `M` acts on `(ι → R) →ₗ[R] M`, and takes the projection
@@ -67,11 +71,14 @@ def PiToModule.fromEnd : Module.End R M →ₗ[R] (ι → R) →ₗ[R] M :=
 #align pi_to_module.from_End PiToModule.fromEnd
 -/
 
+#print PiToModule.fromEnd_apply /-
 theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
     PiToModule.fromEnd R b f w = f (Fintype.total R R b w) :=
   rfl
 #align pi_to_module.from_End_apply PiToModule.fromEnd_apply
+-/
 
+#print PiToModule.fromEnd_apply_single_one /-
 theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M) (i : ι) :
     PiToModule.fromEnd R b f (Pi.single i 1) = f (b i) :=
   by
@@ -80,7 +87,9 @@ theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M
   convert Fintype.total_apply_single R b i 1
   rw [one_smul]
 #align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_one
+-/
 
+#print PiToModule.fromEnd_injective /-
 theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤) :
     Function.Injective (PiToModule.fromEnd R b) :=
   by
@@ -90,6 +99,7 @@ theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤)
     trivial
   exact (LinearMap.congr_fun e m : _)
 #align pi_to_module.from_End_injective PiToModule.fromEnd_injective
+-/
 
 section
 
@@ -105,16 +115,21 @@ def Matrix.Represents (A : Matrix ι ι R) (f : Module.End R M) : Prop :=
 
 variable {b}
 
+#print Matrix.Represents.congr_fun /-
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   LinearMap.congr_fun h x
 #align matrix.represents.congr_fun Matrix.Represents.congr_fun
+-/
 
+#print Matrix.represents_iff /-
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   ⟨fun e x => e.congr_fun x, fun H => LinearMap.ext fun x => H x⟩
 #align matrix.represents_iff Matrix.represents_iff
+-/
 
+#print Matrix.represents_iff' /-
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ j, ∑ i : ι, A i j • b i = f (b j) :=
   by
@@ -128,7 +143,9 @@ theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
       PiToModule.fromMatrix_apply_single_one]
     apply h
 #align matrix.represents_iff' Matrix.represents_iff'
+-/
 
+#print Matrix.Represents.mul /-
 theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A * A').Represents b (f * f') :=
   by
@@ -139,7 +156,9 @@ theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h
   rw [← h'.congr_fun, ← h.congr_fun]
   rfl
 #align matrix.represents.mul Matrix.Represents.mul
+-/
 
+#print Matrix.Represents.one /-
 theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   by
   delta Matrix.Represents PiToModule.fromMatrix
@@ -147,28 +166,38 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   ext
   rfl
 #align matrix.represents.one Matrix.Represents.one
+-/
 
+#print Matrix.Represents.add /-
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
   delta Matrix.Represents at h h' ⊢; rw [map_add, map_add, h, h']
 #align matrix.represents.add Matrix.Represents.add
+-/
 
+#print Matrix.Represents.zero /-
 theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta Matrix.Represents;
   rw [map_zero, map_zero]
 #align matrix.represents.zero Matrix.Represents.zero
+-/
 
+#print Matrix.Represents.smul /-
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h ⊢;
   rw [map_smul, map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
+-/
 
+#print Matrix.Represents.eq /-
 theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : A.Represents b f') : f = f' :=
   PiToModule.fromEnd_injective R b hb (h.symm.trans h')
 #align matrix.represents.eq Matrix.Represents.eq
+-/
 
 variable (b R)
 
+#print Matrix.isRepresentation /-
 /-- The subalgebra of `matrix ι ι R` that consists of matrices that actually represent
 endomorphisms on `M`. -/
 def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
@@ -180,7 +209,9 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
   zero_mem' := ⟨0, Matrix.Represents.zero⟩
   algebraMap_mem' r := ⟨r • 1, Matrix.Represents.one.smul r⟩
 #align matrix.is_representation Matrix.isRepresentation
+-/
 
+#print Matrix.isRepresentation.toEnd /-
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
 noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b →ₐ[R] Module.End R M
     where
@@ -192,18 +223,24 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
   commutes' r :=
     (r • 1 : Matrix.isRepresentation R b).2.choose_spec.Eq hb (Matrix.Represents.one.smul r)
 #align matrix.is_representation.to_End Matrix.isRepresentation.toEnd
+-/
 
+#print Matrix.isRepresentation.toEnd_represents /-
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
   A.2.choose_spec
 #align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_represents
+-/
 
+#print Matrix.isRepresentation.eq_toEnd_of_represents /-
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
     Matrix.isRepresentation.toEnd R b hb A = f :=
   A.2.choose_spec.Eq hb h
 #align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_represents
+-/
 
+#print Matrix.isRepresentation.toEnd_exists_mem_ideal /-
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
   by
@@ -221,7 +258,9 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
     ⟨⟨A, f, this⟩, Matrix.isRepresentation.eq_toEnd_of_represents R b hb ⟨A, f, this⟩ this,
       fun i j => (bM' (b j) i).Prop⟩
 #align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_ideal
+-/
 
+#print Matrix.isRepresentation.toEnd_surjective /-
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=
   by
@@ -230,9 +269,11 @@ theorem Matrix.isRepresentation.toEnd_surjective :
   exact ⟨M, e⟩
   simp
 #align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjective
+-/
 
 end
 
+#print LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul /-
 /-- The **Cayley-Hamilton Theorem** for f.g. modules over arbitrary rings states that for each
 `R`-endomorphism `φ` of an `R`-module `M` such that `φ(M) ≤ I • M` for some ideal `I`, there
 exists some `n` and some `aᵢ ∈ Iⁱ` such that `φⁿ + a₁ φⁿ⁻¹ + ⋯ + aₙ = 0`.
@@ -260,10 +301,13 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
       Subalgebra.coe_zero]
   · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
+-/
 
+#print LinearMap.exists_monic_and_aeval_eq_zero /-
 theorem LinearMap.exists_monic_and_aeval_eq_zero [Module.Finite R M] (f : Module.End R M) :
     ∃ p : R[X], p.Monic ∧ Polynomial.aeval f p = 0 :=
   (LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul R f ⊤ (by simp)).imp
     fun p h => h.imp_right And.right
 #align linear_map.exists_monic_and_aeval_eq_zero LinearMap.exists_monic_and_aeval_eq_zero
+-/

4280f5f3

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -116,7 +116,7 @@ theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
 #align matrix.represents_iff Matrix.represents_iff
 
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
-    A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) :=
+    A.Represents b f ↔ ∀ j, ∑ i : ι, A i j • b i = f (b j) :=
   by
   constructor
   · intro h i

4280f5f3

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -173,7 +173,7 @@ variable (b R)
 endomorphisms on `M`. -/
 def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
     where
-  carrier := { A | ∃ f : Module.End R M, A.Represents b f }
+  carrier := {A | ∃ f : Module.End R M, A.Represents b f}
   mul_mem' := fun A₁ A₂ ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ * f₂, e₁.mul e₂⟩
   one_mem' := ⟨1, Matrix.Represents.one⟩
   add_mem' := fun A₁ A₂ ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ + f₂, e₁.add e₂⟩
@@ -244,21 +244,21 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
     [Module.Finite R M] (f : Module.End R M) (I : Ideal R) (hI : f.range ≤ I • ⊤) :
     ∃ p : R[X], p.Monic ∧ (∀ k, p.coeff k ∈ I ^ (p.natDegree - k)) ∧ Polynomial.aeval f p = 0 := by
   classical
-    cases subsingleton_or_nontrivial R
-    · exact ⟨0, Polynomial.monic_of_subsingleton _, by simp⟩
-    obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ := Module.Finite.out
-    obtain ⟨A, rfl, h⟩ :=
-      Matrix.isRepresentation.toEnd_exists_mem_ideal R (coe : s → M)
-        (by rw [Subtype.range_coe_subtype, Finset.setOf_mem, hs]) f I hI
-    refine' ⟨A.1.charpoly, A.1.charpoly_monic, _, _⟩
-    · rw [A.1.charpoly_natDegree_eq_dim]
-      exact coeff_charpoly_mem_ideal_pow h
-    · rw [Polynomial.aeval_algHom_apply, ← map_zero (Matrix.isRepresentation.toEnd R coe _)]
-      congr 1
-      ext1
-      rw [Polynomial.aeval_subalgebra_coe, Subtype.val_eq_coe, Matrix.aeval_self_charpoly,
-        Subalgebra.coe_zero]
-    · infer_instance
+  cases subsingleton_or_nontrivial R
+  · exact ⟨0, Polynomial.monic_of_subsingleton _, by simp⟩
+  obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ := Module.Finite.out
+  obtain ⟨A, rfl, h⟩ :=
+    Matrix.isRepresentation.toEnd_exists_mem_ideal R (coe : s → M)
+      (by rw [Subtype.range_coe_subtype, Finset.setOf_mem, hs]) f I hI
+  refine' ⟨A.1.charpoly, A.1.charpoly_monic, _, _⟩
+  · rw [A.1.charpoly_natDegree_eq_dim]
+    exact coeff_charpoly_mem_ideal_pow h
+  · rw [Polynomial.aeval_algHom_apply, ← map_zero (Matrix.isRepresentation.toEnd R coe _)]
+    congr 1
+    ext1
+    rw [Polynomial.aeval_subalgebra_coe, Subtype.val_eq_coe, Matrix.aeval_self_charpoly,
+      Subalgebra.coe_zero]
+  · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
 
 theorem LinearMap.exists_monic_and_aeval_eq_zero [Module.Finite R M] (f : Module.End R M) :

4280f5f3

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -121,7 +121,7 @@ theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
   constructor
   · intro h i
     have := LinearMap.congr_fun h (Pi.single i 1)
-    rwa [PiToModule.fromEnd_apply_single_one, PiToModule.fromMatrix_apply_single_one] at this
+    rwa [PiToModule.fromEnd_apply_single_one, PiToModule.fromMatrix_apply_single_one] at this 
   · intro h
     ext
     simp_rw [LinearMap.comp_apply, LinearMap.coe_single, PiToModule.fromEnd_apply_single_one,
@@ -150,7 +150,7 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
 
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
-  delta Matrix.Represents at h h'⊢; rw [map_add, map_add, h, h']
+  delta Matrix.Represents at h h' ⊢; rw [map_add, map_add, h, h']
 #align matrix.represents.add Matrix.Represents.add
 
 theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta Matrix.Represents;
@@ -158,7 +158,7 @@ theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta
 #align matrix.represents.zero Matrix.Represents.zero
 
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
-    (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h⊢;
+    (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h ⊢;
   rw [map_smul, map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
 
@@ -216,7 +216,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
     dsimp [A]
     intro j
     specialize hbM' (b j)
-    rwa [Ideal.finsuppTotal_apply_eq_of_fintype] at hbM'
+    rwa [Ideal.finsuppTotal_apply_eq_of_fintype] at hbM' 
   exact
     ⟨⟨A, f, this⟩, Matrix.isRepresentation.eq_toEnd_of_represents R b hb ⟨A, f, this⟩ this,
       fun i j => (bM' (b j) i).Prop⟩

4280f5f3

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -261,11 +261,9 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
     · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
 
-#print LinearMap.exists_monic_and_aeval_eq_zero /-
 theorem LinearMap.exists_monic_and_aeval_eq_zero [Module.Finite R M] (f : Module.End R M) :
     ∃ p : R[X], p.Monic ∧ Polynomial.aeval f p = 0 :=
   (LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul R f ⊤ (by simp)).imp
     fun p h => h.imp_right And.right
 #align linear_map.exists_monic_and_aeval_eq_zero LinearMap.exists_monic_and_aeval_eq_zero
--/

4280f5f3

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -35,9 +35,9 @@ variable {M : Type _} [AddCommGroup M] (R : Type _) [CommRing R] [Module R M] (I
 
 variable (b : ι → M) (hb : Submodule.span R (Set.range b) = ⊤)
 
-open BigOperators
+open scoped BigOperators
 
-open Polynomial
+open scoped Polynomial
 
 #print PiToModule.fromMatrix /-
 /-- The composition of a matrix (as an endomporphism of `ι → R`) with the projection

4280f5f3

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -47,17 +47,11 @@ def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R)
 #align pi_to_module.from_matrix PiToModule.fromMatrix
 -/
 
-/- warning: pi_to_module.from_matrix_apply -> PiToModule.fromMatrix_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply PiToModule.fromMatrix_applyₓ'. -/
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
     PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
   rfl
 #align pi_to_module.from_matrix_apply PiToModule.fromMatrix_apply
 
-/- warning: pi_to_module.from_matrix_apply_single_one -> PiToModule.fromMatrix_apply_single_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_oneₓ'. -/
 theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι ι R) (j : ι) :
     PiToModule.fromMatrix R b A (Pi.single j 1) = ∑ i : ι, A i j • b i :=
   by
@@ -73,17 +67,11 @@ def PiToModule.fromEnd : Module.End R M →ₗ[R] (ι → R) →ₗ[R] M :=
 #align pi_to_module.from_End PiToModule.fromEnd
 -/
 
-/- warning: pi_to_module.from_End_apply -> PiToModule.fromEnd_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply PiToModule.fromEnd_applyₓ'. -/
 theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
     PiToModule.fromEnd R b f w = f (Fintype.total R R b w) :=
   rfl
 #align pi_to_module.from_End_apply PiToModule.fromEnd_apply
 
-/- warning: pi_to_module.from_End_apply_single_one -> PiToModule.fromEnd_apply_single_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_oneₓ'. -/
 theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M) (i : ι) :
     PiToModule.fromEnd R b f (Pi.single i 1) = f (b i) :=
   by
@@ -93,9 +81,6 @@ theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M
   rw [one_smul]
 #align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_one
 
-/- warning: pi_to_module.from_End_injective -> PiToModule.fromEnd_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_injective PiToModule.fromEnd_injectiveₓ'. -/
 theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤) :
     Function.Injective (PiToModule.fromEnd R b) :=
   by
@@ -120,25 +105,16 @@ def Matrix.Represents (A : Matrix ι ι R) (f : Module.End R M) : Prop :=
 
 variable {b}
 
-/- warning: matrix.represents.congr_fun -> Matrix.Represents.congr_fun is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.represents.congr_fun Matrix.Represents.congr_funₓ'. -/
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   LinearMap.congr_fun h x
 #align matrix.represents.congr_fun Matrix.Represents.congr_fun
 
-/- warning: matrix.represents_iff -> Matrix.represents_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.represents_iff Matrix.represents_iffₓ'. -/
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   ⟨fun e x => e.congr_fun x, fun H => LinearMap.ext fun x => H x⟩
 #align matrix.represents_iff Matrix.represents_iff
 
-/- warning: matrix.represents_iff' -> Matrix.represents_iff' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.represents_iff' Matrix.represents_iff'ₓ'. -/
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) :=
   by
@@ -153,12 +129,6 @@ theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     apply h
 #align matrix.represents_iff' Matrix.represents_iff'
 
-/- warning: matrix.represents.mul -> Matrix.Represents.mul is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align matrix.represents.mul Matrix.Represents.mulₓ'. -/
 theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A * A').Represents b (f * f') :=
   by
@@ -170,12 +140,6 @@ theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h
   rfl
 #align matrix.represents.mul Matrix.Represents.mul
 
-/- warning: matrix.represents.one -> Matrix.Represents.one is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι], Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 1 (OfNat.mk.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 1 (One.one.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.hasOne.{u3, u1} ι R (fun (a : ι) (b : ι) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddMonoidWithOne.toOne.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (AddCommGroupWithOne.toAddGroupWithOne.{u3} R (Ring.toAddCommGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_3))))))))) (OfNat.ofNat.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (OfNat.mk.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (One.one.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.End.hasOne.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))))
-but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι], Matrix.Represents.{u3, u2, u1} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) (Matrix.one.{u1, u3} ι R (fun (a : ι) (b : ι) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (OfNat.ofNat.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (One.toOfNat1.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.instOneEnd.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))
-Case conversion may be inaccurate. Consider using '#align matrix.represents.one Matrix.Represents.oneₓ'. -/
 theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   by
   delta Matrix.Represents PiToModule.fromMatrix
@@ -184,38 +148,20 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   rfl
 #align matrix.represents.one Matrix.Represents.one
 
-/- warning: matrix.represents.add -> Matrix.Represents.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.represents.add Matrix.Represents.addₓ'. -/
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
   delta Matrix.Represents at h h'⊢; rw [map_add, map_add, h, h']
 #align matrix.represents.add Matrix.Represents.add
 
-/- warning: matrix.represents.zero -> Matrix.Represents.zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align matrix.represents.zero Matrix.Represents.zeroₓ'. -/
 theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta Matrix.Represents;
   rw [map_zero, map_zero]
 #align matrix.represents.zero Matrix.Represents.zero
 
-/- warning: matrix.represents.smul -> Matrix.Represents.smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.represents.smul Matrix.Represents.smulₓ'. -/
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h⊢;
   rw [map_smul, map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
 
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-Case conversion may be inaccurate. Consider using '#align matrix.represents.eq Matrix.Represents.eqₓ'. -/
 theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : A.Represents b f') : f = f' :=
   PiToModule.fromEnd_injective R b hb (h.symm.trans h')
@@ -223,12 +169,6 @@ theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A
 
 variable (b R)
 
-/- warning: matrix.is_representation -> Matrix.isRepresentation is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align matrix.is_representation Matrix.isRepresentationₓ'. -/
 /-- The subalgebra of `matrix ι ι R` that consists of matrices that actually represent
 endomorphisms on `M`. -/
 def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
@@ -241,9 +181,6 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
   algebraMap_mem' r := ⟨r • 1, Matrix.Represents.one.smul r⟩
 #align matrix.is_representation Matrix.isRepresentation
 
-/- warning: matrix.is_representation.to_End -> Matrix.isRepresentation.toEnd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End Matrix.isRepresentation.toEndₓ'. -/
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
 noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b →ₐ[R] Module.End R M
     where
@@ -256,26 +193,17 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
     (r • 1 : Matrix.isRepresentation R b).2.choose_spec.Eq hb (Matrix.Represents.one.smul r)
 #align matrix.is_representation.to_End Matrix.isRepresentation.toEnd
 
-/- warning: matrix.is_representation.to_End_represents -> Matrix.isRepresentation.toEnd_represents is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_representsₓ'. -/
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
   A.2.choose_spec
 #align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_represents
 
-/- warning: matrix.is_representation.eq_to_End_of_represents -> Matrix.isRepresentation.eq_toEnd_of_represents is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_representsₓ'. -/
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
     Matrix.isRepresentation.toEnd R b hb A = f :=
   A.2.choose_spec.Eq hb h
 #align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_represents
 
-/- warning: matrix.is_representation.to_End_exists_mem_ideal -> Matrix.isRepresentation.toEnd_exists_mem_ideal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_idealₓ'. -/
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
   by
@@ -294,9 +222,6 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
       fun i j => (bM' (b j) i).Prop⟩
 #align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_ideal
 
-/- warning: matrix.is_representation.to_End_surjective -> Matrix.isRepresentation.toEnd_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjectiveₓ'. -/
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=
   by
@@ -308,9 +233,6 @@ theorem Matrix.isRepresentation.toEnd_surjective :
 
 end
 
-/- warning: linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul -> LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smulₓ'. -/
 /-- The **Cayley-Hamilton Theorem** for f.g. modules over arbitrary rings states that for each
 `R`-endomorphism `φ` of an `R`-module `M` such that `φ(M) ≤ I • M` for some ideal `I`, there
 exists some `n` and some `aᵢ ∈ Iⁱ` such that `φⁿ + a₁ φⁿ⁻¹ + ⋯ + aₙ = 0`.

4280f5f3

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -101,9 +101,7 @@ theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤)
   by
   intro x y e
   ext m
-  obtain ⟨m, rfl⟩ : m ∈ (Fintype.total R R b).range :=
-    by
-    rw [(Fintype.range_total R b).trans hb]
+  obtain ⟨m, rfl⟩ : m ∈ (Fintype.total R R b).range := by rw [(Fintype.range_total R b).trans hb];
     trivial
   exact (LinearMap.congr_fun e m : _)
 #align pi_to_module.from_End_injective PiToModule.fromEnd_injective
@@ -281,9 +279,7 @@ Case conversion may be inaccurate. Consider using '#align matrix.is_representati
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
   by
-  have : ∀ x, f x ∈ (Ideal.finsuppTotal ι M I b).range :=
-    by
-    rw [Ideal.range_finsuppTotal, hb]
+  have : ∀ x, f x ∈ (Ideal.finsuppTotal ι M I b).range := by rw [Ideal.range_finsuppTotal, hb];
     exact fun x => hI (f.mem_range_self x)
   choose bM' hbM'
   let A : Matrix ι ι R := fun i j => bM' (b j) i

4280f5f3

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -48,10 +48,7 @@ def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R)
 -/
 
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(NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Matrix.{u1, u1, u3} ι ι R) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R 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(smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply PiToModule.fromMatrix_applyₓ'. -/
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
     PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
@@ -59,10 +56,7 @@ theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : 
 #align pi_to_module.from_matrix_apply PiToModule.fromMatrix_apply
 
 /- warning: pi_to_module.from_matrix_apply_single_one -> PiToModule.fromMatrix_apply_single_one is a dubious translation:
-lean 3 declaration is
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(CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R 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(Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, max (max u3 u1) u2} R R (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R 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(SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromMatrix.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_oneₓ'. -/
 theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι ι R) (j : ι) :
     PiToModule.fromMatrix R b A (Pi.single j 1) = ∑ i : ι, A i j • b i :=
@@ -80,10 +74,7 @@ def PiToModule.fromEnd : Module.End R M →ₗ[R] (ι → R) →ₗ[R] M :=
 -/
 
 /- warning: pi_to_module.from_End_apply -> PiToModule.fromEnd_apply is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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(CommRing.toCommSemiring.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) w))
+<too large>
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply PiToModule.fromEnd_applyₓ'. -/
 theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
     PiToModule.fromEnd R b f w = f (Fintype.total R R b w) :=
@@ -91,10 +82,7 @@ theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
 #align pi_to_module.from_End_apply PiToModule.fromEnd_apply
 
 /- warning: pi_to_module.from_End_apply_single_one -> PiToModule.fromEnd_apply_single_one is a dubious translation:
-lean 3 declaration is
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(fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R 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(CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_oneₓ'. -/
 theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M) (i : ι) :
     PiToModule.fromEnd R b f (Pi.single i 1) = f (b i) :=
@@ -106,10 +94,7 @@ theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M
 #align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_one
 
 /- warning: pi_to_module.from_End_injective -> PiToModule.fromEnd_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_injective PiToModule.fromEnd_injectiveₓ'. -/
 theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤) :
     Function.Injective (PiToModule.fromEnd R b) :=
@@ -138,10 +123,7 @@ def Matrix.Represents (A : Matrix ι ι R) (f : Module.End R M) : Prop :=
 variable {b}
 
 /- warning: matrix.represents.congr_fun -> Matrix.Represents.congr_fun is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.represents.congr_fun Matrix.Represents.congr_funₓ'. -/
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
@@ -149,10 +131,7 @@ theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h
 #align matrix.represents.congr_fun Matrix.Represents.congr_fun
 
 /- warning: matrix.represents_iff -> Matrix.represents_iff is a dubious translation:
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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) x)))
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(smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.represents_iff Matrix.represents_iffₓ'. -/
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
@@ -160,10 +139,7 @@ theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
 #align matrix.represents_iff Matrix.represents_iff
 
 /- warning: matrix.represents_iff' -> Matrix.represents_iff' is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.represents_iff' Matrix.represents_iff'ₓ'. -/
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) :=
@@ -211,10 +187,7 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
 #align matrix.represents.one Matrix.Represents.one
 
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 Case conversion may be inaccurate. Consider using '#align matrix.represents.add Matrix.Represents.addₓ'. -/
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
@@ -232,10 +205,7 @@ theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta
 #align matrix.represents.zero Matrix.Represents.zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.represents.smul Matrix.Represents.smulₓ'. -/
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h⊢;
@@ -274,10 +244,7 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
 #align matrix.is_representation Matrix.isRepresentation
 
 /- warning: matrix.is_representation.to_End -> Matrix.isRepresentation.toEnd is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End Matrix.isRepresentation.toEndₓ'. -/
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
 noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b →ₐ[R] Module.End R M
@@ -292,10 +259,7 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
 #align matrix.is_representation.to_End Matrix.isRepresentation.toEnd
 
 /- warning: matrix.is_representation.to_End_represents -> Matrix.isRepresentation.toEnd_represents is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_representsₓ'. -/
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
@@ -303,10 +267,7 @@ theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R
 #align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_represents
 
 /- warning: matrix.is_representation.eq_to_End_of_represents -> Matrix.isRepresentation.eq_toEnd_of_represents is a dubious translation:
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(b : ι) => _inst_5 a b)) A) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_representsₓ'. -/
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
@@ -315,10 +276,7 @@ theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentat
 #align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_represents
 
 /- warning: matrix.is_representation.to_End_exists_mem_ideal -> Matrix.isRepresentation.toEnd_exists_mem_ideal is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_idealₓ'. -/
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
@@ -341,10 +299,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
 #align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_ideal
 
 /- warning: matrix.is_representation.to_End_surjective -> Matrix.isRepresentation.toEnd_surjective is a dubious translation:
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(b : ι) => _inst_5 a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjectiveₓ'. -/
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=
@@ -358,10 +313,7 @@ theorem Matrix.isRepresentation.toEnd_surjective :
 end
 
 /- warning: linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul -> LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul is a dubious translation:
-lean 3 declaration is
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(Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instHPow.{u2, 0} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_3) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p) k))) (Eq.{succ u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (fun (_x : AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) 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-but is expected to have type
-  forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M 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(CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smulₓ'. -/
 /-- The **Cayley-Hamilton Theorem** for f.g. modules over arbitrary rings states that for each
 `R`-endomorphism `φ` of an `R`-module `M` such that `φ(M) ≤ I • M` for some ideal `I`, there

4280f5f3

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -51,7 +51,7 @@ def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R)
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u1} ι] (A : Matrix.{u1, u1, u3} ι ι R) (w : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) 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(Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Matrix.{u1, u1, u3} ι ι R) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max (max u1 u3) u2} R R (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) (Matrix.mulVec.{u3, u1, u1} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_1 A w))
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (w : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) A) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (LinearMap.{u2, u2, max u2 u3, max u1 u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Matrix.{u3, u3, u2} ι ι R) (fun (_x : Matrix.{u3, u3, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A w))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (w : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) A) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (LinearMap.{u2, u2, max u2 u3, max u1 u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M 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(SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> M) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, max (max u2 u1) u3} R R (ι -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A w))
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply PiToModule.fromMatrix_applyₓ'. -/
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
     PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
@@ -62,7 +62,7 @@ theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : 
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u1} ι] (A : Matrix.{u1, u1, u3} ι ι R) (j : ι), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (coeFn.{max (succ (max u1 u3)) (succ (max (max u1 u3) u2)), max (succ (max u1 u3)) (succ (max (max u1 u3) u2))} (LinearMap.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Matrix.{u1, u1, u3} ι ι R) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (PiToModule.fromMatrix.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) j (OfNat.ofNat.{u3} R 1 (OfNat.mk.{u3} R 1 (One.one.{u3} R (AddMonoidWithOne.toOne.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (AddCommGroupWithOne.toAddGroupWithOne.{u3} R (Ring.toAddCommGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_3)))))))))) (Finset.sum.{u2, u1} M ι (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.univ.{u1} ι _inst_1) (fun (i : ι) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (A i j) (b i)))
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Pi.single.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) A) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Matrix.{u3, u3, u2} ι ι R) (fun (_x : Matrix.{u3, u3, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, max (max u3 u1) u2} R R (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromMatrix.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i)))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) (Pi.single.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) A) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Matrix.{u3, u3, u2} ι ι R) (fun (_x : Matrix.{u3, u3, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, max (max u3 u1) u2} R R (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromMatrix.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i)))
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_oneₓ'. -/
 theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι ι R) (j : ι) :
     PiToModule.fromMatrix R b A (Pi.single j 1) = ∑ i : ι, A i j • b i :=
@@ -83,7 +83,7 @@ def PiToModule.fromEnd : Module.End R M →ₗ[R] (ι → R) →ₗ[R] M :=
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (coeFn.{max (succ u2) (succ (max (max u1 u3) u2)), max (succ u2) (succ (max (max u1 u3) u2))} (LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))))) => (ι -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max (max u1 u3) u2} R R (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) w))
 but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (f : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) => LinearMap.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4) f) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, max u1 u3, u2} R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Pi.module.{u1, u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) w))
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (f : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) => LinearMap.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) 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(fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (max (succ u1) (succ u2)) (succ u3)} (LinearMap.{u3, u3, u2, max u2 u1 u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R 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(SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 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(RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Pi.module.{u1, u2, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.module.{u1, u3, u3} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) w))
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply PiToModule.fromEnd_applyₓ'. -/
 theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
     PiToModule.fromEnd R b f w = f (Fintype.total R R b w) :=
@@ -94,7 +94,7 @@ theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u1} ι] (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (i : ι), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (coeFn.{max (succ u2) (succ (max (max u1 u3) u2)), max (succ u2) (succ (max (max u1 u3) u2))} (LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R 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(CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} 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(NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (PiToModule.fromEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b) f) (Pi.single.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) i (OfNat.ofNat.{u3} R 1 (OfNat.mk.{u3} R 1 (One.one.{u3} R (AddMonoidWithOne.toOne.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (AddCommGroupWithOne.toAddGroupWithOne.{u3} R (Ring.toAddCommGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_3)))))))))) (coeFn.{succ u2, succ u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) f (b i))
 but is expected to have type
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_inst_3))))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (fun (_x : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max (max u3 u1) u2} R R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b) f) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) i (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b i))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) (Pi.single.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) i (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b) f) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) i (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b i))
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_oneₓ'. -/
 theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M) (i : ι) :
     PiToModule.fromEnd R b f (Pi.single i 1) = f (b i) :=
@@ -109,7 +109,7 @@ theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M), (Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Function.Injective.{succ u2, max (succ (max u1 u3)) (succ u2)} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (coeFn.{max (succ u2) (succ (max (max u1 u3) u2)), max (succ u2) (succ (max (max u1 u3) u2))} (LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (PiToModule.fromEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b)))
 but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (b : ι -> M), (Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.span.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 (Set.range.{u3, succ u1} M ι b)) (Top.top.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4))) -> (Function.Injective.{succ u3, max (max (succ u1) (succ u3)) (succ u2)} (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u2, u2, u3, max u3 u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u1 u2, u3} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, max (max u1 u3) u2} R R (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u1 u2, u3} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromEnd.{u1, u3, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b)))
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (b : ι -> M), (Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.span.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 (Set.range.{u3, succ u1} M ι b)) (Top.top.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4))) -> (Function.Injective.{succ u3, max (max (succ u1) (succ u3)) (succ u2)} (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (max (succ u1) (succ u3)) (succ u2)} (LinearMap.{u2, u2, u3, max u3 u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M 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(a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u1 u2, u3} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4))))) (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (fun (_x : Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) => LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, max (max u1 u3) u2} R R (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.addCommMonoid.{u2, u2, max u1 u2, u3} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u1 u2, u3} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u3} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u3} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u3} M (SubNegZeroMonoid.toNegZeroClass.{u3} M (SubtractionMonoid.toSubNegZeroMonoid.{u3} M (SubtractionCommMonoid.toSubtractionMonoid.{u3} M (AddCommGroup.toDivisionAddCommMonoid.{u3} M _inst_2))))) (Module.toMulActionWithZero.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromEnd.{u1, u3, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b)))
 Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_injective PiToModule.fromEnd_injectiveₓ'. -/
 theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤) :
     Function.Injective (PiToModule.fromEnd R b) :=
@@ -141,7 +141,7 @@ variable {b}
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (x : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max (max u1 u3) u2} R R (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) x)))
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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(fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) b) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u1) (succ u3), max (max (succ u2) (succ u1)) (succ u3)} (LinearMap.{u2, u2, max u3 u1, max u1 u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => 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(CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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(CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> M) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, max (max u2 u1) u3} R R (ι -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) x)))
 Case conversion may be inaccurate. Consider using '#align matrix.represents.congr_fun Matrix.Represents.congr_funₓ'. -/
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
@@ -152,7 +152,7 @@ theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (x : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) x)))
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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(fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) b) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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_inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) x)))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (ι -> M) (fun (_x : ι -> M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : ι -> M) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, max (max u2 u1) u3} R R (ι -> M) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u1} ι (fun (ᾰ : ι) => M) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2)) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Pi.module.{u3, u1, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14558 : ι) => M) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (fun (i : ι) => _inst_4)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Finsupp._hyg.14570 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) x)))
 Case conversion may be inaccurate. Consider using '#align matrix.represents_iff Matrix.represents_iffₓ'. -/
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
@@ -163,7 +163,7 @@ theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (j : ι), Eq.{succ u2} M (Finset.sum.{u2, u1} M ι (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.univ.{u1} ι _inst_1) (fun (i : ι) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (A i j) (b i))) (coeFn.{succ u2, succ u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) f (b j)))
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (j : ι), Eq.{succ u1} M (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b j)))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (j : ι), Eq.{succ u1} M (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b j)))
 Case conversion may be inaccurate. Consider using '#align matrix.represents_iff' Matrix.represents_iff'ₓ'. -/
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) :=
@@ -295,7 +295,7 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
 lean 3 declaration is
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(max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R 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_inst_5 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Matrix.{u1, u1, u3} ι ι R) (CoeTCₓ.coe.{succ (max u1 u3), succ (max u1 u3)} (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} 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_inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
 but is expected to have type
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(CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_representsₓ'. -/
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
@@ -306,7 +306,7 @@ theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R
 lean 3 declaration is
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 but is expected to have type
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R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R 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(b : ι) => _inst_5 a b)) A) f)
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u3} ι] (A : Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) 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_inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A) f)
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_representsₓ'. -/
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
@@ -318,7 +318,7 @@ theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentat
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι] (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))), (LE.le.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) 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_inst_3))) f) (SMul.smul.{u3, u2} (Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) I (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) -> (Exists.{succ (max u1 u3)} (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) 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(Module.End.algebra.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) => (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => 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-> (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) ([anonymous].{u3, max u1 u3, u2} R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) M_1 i j) I)))
 but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι] (f : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))), (LE.le.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Preorder.toLE.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} 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+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) M_1 i j) I)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_idealₓ'. -/
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
@@ -344,7 +344,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
 lean 3 declaration is
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 but is expected to have type
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(b : ι) => _inst_5 a b)))
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjectiveₓ'. -/
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=
@@ -361,7 +361,7 @@ end
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toHasLe.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (SetLike.partialOrder.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) f) (SMul.smul.{u2, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) I (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasTop.{u2, u1} R M (Ring.toSemiring.{u2} R 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(Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instHPow.{u2, 0} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_3) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p) k))) (Eq.{succ u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (fun (_x : AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) => (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) -> (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) ([anonymous].{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 0 (OfNat.mk.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 0 (Zero.zero.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.hasZero.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.completeLattice.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) f) (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) I (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) -> (Exists.{succ u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (fun (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => And (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p) (And (forall (k : Nat), Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p) k))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) (SMulZeroClass.toSMul.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AddMonoid.toZero.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AddMonoid.toAddZeroClass.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 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(CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 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(CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} 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(Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))))))
+  forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.completeLattice.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) f) (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) I (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) -> (Exists.{succ u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (fun (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => And (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p) (And (forall (k : Nat), Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_3) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p) k))) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} 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(CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) 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(Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 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(CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R 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(NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smulₓ'. -/
 /-- The **Cayley-Hamilton Theorem** for f.g. modules over arbitrary rings states that for each
 `R`-endomorphism `φ` of an `R`-module `M` such that `φ(M) ≤ I • M` for some ideal `I`, there

4280f5f3

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.linear_map
-! leanprover-community/mathlib commit 62c0a4ef1441edb463095ea02a06e87f3dfe135c
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Matrix.ToLin
 
 # Calyley-Hamilton theorem for f.g. modules.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a fixed finite spanning set `b : ι → M` of a `R`-module `M`, we say that a matrix `M`
 represents an endomorphism `f : M →ₗ[R] M` if the matrix as an endomorphism of `ι → R` commutes
 with `f` via the projection `(ι → R) →ₗ[R] M` given by `b`.
@@ -274,7 +277,7 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M), (Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (forall [_inst_5 : DecidableEq.{succ u1} ι], AlgHom.{u3, max u1 u3, u2} R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Subalgebra.algebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.algebra.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))
 but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M), (Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (forall [_inst_5 : DecidableEq.{succ u1} ι], AlgHom.{u3, max u1 u3, u2} R (Subtype.{succ (max u1 u3)} (Matrix.{u1, u1, u3} ι ι R) (fun (x : Matrix.{u1, u1, u3} ι ι R) => Membership.mem.{max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M), (Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (forall [_inst_5 : DecidableEq.{succ u1} ι], AlgHom.{u3, max u1 u3, u2} R (Subtype.{succ (max u1 u3)} (Matrix.{u1, u1, u3} ι ι R) (fun (x : Matrix.{u1, u1, u3} ι ι R) => Membership.mem.{max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Subalgebra.algebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End Matrix.isRepresentation.toEndₓ'. -/
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
 noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b →ₐ[R] Module.End R M
@@ -292,7 +295,7 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι] (A : coeSort.{succ (max u1 u3), succ (succ 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(Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) -> (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) ([anonymous].{u3, max u1 u3, u2} R (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Subalgebra.algebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.algebra.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) (Matrix.isRepresentation.toEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, u1, max (max u3 u1) u2} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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b (fun (a : ι) (b : ι) => _inst_5 a b))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} 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(CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) 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(CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_representsₓ'. -/
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
@@ -303,7 +306,7 @@ theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R
 lean 3 declaration is
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(b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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_inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Subalgebra.algebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.algebra.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) (Matrix.isRepresentation.toEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A) f)
 but is expected to have type
-  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, max u3 u2, u1} R (Subtype.{succ (max u3 u2)} (Matrix.{u3, u3, u2} ι ι R) (fun (x : Matrix.{u3, u3, u2} ι ι R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Subalgebra.algebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A) f)
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_representsₓ'. -/
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
@@ -315,7 +318,7 @@ theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentat
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι] (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))), (LE.le.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) 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b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (SetLike.hasMem.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) 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 but is expected to have type
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_inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) M_1 i j) I)))
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u3} R _inst_3) (Subalgebra.toSemiring.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u3, u2} R M 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(Matrix.{u1, u1, u3} ι ι R) (fun (x : Matrix.{u1, u1, u3} ι ι R) => Membership.mem.{max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (SetLike.instMembership.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) x (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R 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(Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (Matrix.isRepresentation.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.instAlgebraEndToSemiringSemiring.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))))) (Matrix.isRepresentation.toEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) M_1) f) (forall (i : ι) (j : ι), Membership.mem.{u3, u3} R (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) (SetLike.instMembership.{u3, u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))) R (Submodule.setLike.{u3, u3} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))) (Subtype.val.{max (succ u1) (succ u3)} (Matrix.{u1, u1, u3} ι ι R) (fun (x : Matrix.{u1, u1, u3} ι ι R) => Membership.mem.{max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => 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 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_idealₓ'. -/
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
@@ -341,7 +344,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι], Function.Surjective.{succ (max u1 u3), 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 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R) => Membership.mem.{max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (SetLike.instMembership.{max u3 u2, max u3 u2} (Subalgebra.{u2, max u2 u3} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (Subalgebra.instSetLikeSubalgebra.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) x (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Subalgebra.toSemiring.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommRing.toCommSemiring.{u2} R _inst_3) (Matrix.semiring.{u2, u3} ι R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Matrix.isRepresentation.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 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+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(b : ι) => _inst_5 a b)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjectiveₓ'. -/
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=

62c0a4ef

bump to nightly-2023-05-22-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

a4206c98

Diff

@@ -36,17 +36,31 @@ open BigOperators
 
 open Polynomial
 
+#print PiToModule.fromMatrix /-
 /-- The composition of a matrix (as an endomporphism of `ι → R`) with the projection
 `(ι → R) →ₗ[R] M`.  -/
 def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R) →ₗ[R] M :=
   (LinearMap.llcomp R _ _ _ (Fintype.total R R b)).comp algEquivMatrix'.symm.toLinearMap
 #align pi_to_module.from_matrix PiToModule.fromMatrix
+-/
 
+/- warning: pi_to_module.from_matrix_apply -> PiToModule.fromMatrix_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u1} ι] (A : Matrix.{u1, u1, u3} ι ι R) (w : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) 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_inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Matrix.{u1, u1, u3} ι ι R) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) (Matrix.mulVec.{u3, u1, u1} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_1 A w))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (w : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) A) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (LinearMap.{u2, u2, max u2 u3, max u1 u3 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, max u3 u2, u1} R R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (Matrix.{u3, u3, u2} ι ι R) (fun (_x : Matrix.{u3, u3, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Matrix.{u3, u3, u2} ι ι R) => LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M 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(smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Fintype.total.{u3, u1, u2, u2} ι M R _inst_1 (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) 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+Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply PiToModule.fromMatrix_applyₓ'. -/
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
     PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
   rfl
 #align pi_to_module.from_matrix_apply PiToModule.fromMatrix_apply
 
+/- warning: pi_to_module.from_matrix_apply_single_one -> PiToModule.fromMatrix_apply_single_one is a dubious translation:
+lean 3 declaration is
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_inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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(fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, max (max u1 u3) u2} R R (Matrix.{u1, u1, u3} ι ι R) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Matrix.addCommMonoid.{u3, u1, u1} ι ι R (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Matrix.module.{u3, u1, u1, u3} ι ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromMatrix._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (PiToModule.fromMatrix.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) j (OfNat.ofNat.{u3} R 1 (OfNat.mk.{u3} R 1 (One.one.{u3} R (AddMonoidWithOne.toOne.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (AddCommGroupWithOne.toAddGroupWithOne.{u3} R (Ring.toAddCommGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_3)))))))))) (Finset.sum.{u2, u1} M ι (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.univ.{u1} ι _inst_1) (fun (i : ι) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (A i j) (b i)))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (A : Matrix.{u3, u3, u2} ι ι R) (j : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Pi.single.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), max (succ u3) (succ u2), succ u1} ((fun 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(Pi.addCommMonoid.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u3 u2, max (max u3 u1) u2} R R (Matrix.{u3, u3, u2} ι ι R) (LinearMap.{u2, u2, max u3 u2, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Pi.module.{u3, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.130 : ι) => R) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (LinearMap.addCommMonoid.{u2, u2, max u3 u2, u1} R R (ι -> R) M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Pi.addCommMonoid.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromMatrix.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b)) A) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) j (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i)))
+Case conversion may be inaccurate. Consider using '#align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_oneₓ'. -/
 theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι ι R) (j : ι) :
     PiToModule.fromMatrix R b A (Pi.single j 1) = ∑ i : ι, A i j • b i :=
   by
@@ -54,17 +68,31 @@ theorem PiToModule.fromMatrix_apply_single_one [DecidableEq ι] (A : Matrix ι 
   simp_rw [mul_one]
 #align pi_to_module.from_matrix_apply_single_one PiToModule.fromMatrix_apply_single_one
 
+#print PiToModule.fromEnd /-
 /-- The endomorphisms of `M` acts on `(ι → R) →ₗ[R] M`, and takes the projection
 to a `(ι → R) →ₗ[R] M`. -/
 def PiToModule.fromEnd : Module.End R M →ₗ[R] (ι → R) →ₗ[R] M :=
   LinearMap.lcomp _ _ (Fintype.total R R b)
 #align pi_to_module.from_End PiToModule.fromEnd
+-/
 
+/- warning: pi_to_module.from_End_apply -> PiToModule.fromEnd_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) => (ι -> R) -> M) (LinearMap.hasCoeToFun.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (coeFn.{max (succ u2) (succ (max (max u1 u3) u2)), max (succ u2) (succ (max (max u1 u3) u2))} (LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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(AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R 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(CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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_inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) w))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (f : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (w : ι -> R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) w) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ u3), succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Module.End.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) => LinearMap.{u3, u3, max u1 u3, u2} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) 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+Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply PiToModule.fromEnd_applyₓ'. -/
 theorem PiToModule.fromEnd_apply (f : Module.End R M) (w : ι → R) :
     PiToModule.fromEnd R b f w = f (Fintype.total R R b w) :=
   rfl
 #align pi_to_module.from_End_apply PiToModule.fromEnd_apply
 
+/- warning: pi_to_module.from_End_apply_single_one -> PiToModule.fromEnd_apply_single_one is a dubious translation:
+lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) [_inst_5 : DecidableEq.{succ u3} ι] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Pi.single.{u3, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) i (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(fun (i : ι) => Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (PiToModule.fromEnd.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b) f) (Pi.single.{u3, u2} ι (fun (ᾰ : ι) => R) (fun (a : ι) (b : ι) => _inst_5 a b) (fun (i : ι) => CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) i (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b i))
+Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_oneₓ'. -/
 theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M) (i : ι) :
     PiToModule.fromEnd R b f (Pi.single i 1) = f (b i) :=
   by
@@ -74,6 +102,12 @@ theorem PiToModule.fromEnd_apply_single_one [DecidableEq ι] (f : Module.End R M
   rw [one_smul]
 #align pi_to_module.from_End_apply_single_one PiToModule.fromEnd_apply_single_one
 
+/- warning: pi_to_module.from_End_injective -> PiToModule.fromEnd_injective is a dubious translation:
+lean 3 declaration is
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_inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) (fun (_x : LinearMap.{u3, u3, u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) 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R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4))) => (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, u2, max (max u1 u3) u2} R R (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (LinearMap.addCommMonoid.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.addCommMonoid.{u3, u3, max u1 u3, u2} R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (LinearMap.module.{u3, u3, u3, u2, u2} R R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_1.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (PiToModule.fromEnd._proof_2.{u2, u3} M _inst_2 R _inst_3 _inst_4)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (PiToModule.fromEnd.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b)))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] (b : ι -> M), (Eq.{succ u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.span.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4 (Set.range.{u3, succ u1} M ι b)) (Top.top.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4))) -> (Function.Injective.{succ u3, max (max (succ u1) (succ u3)) (succ u2)} (Module.End.{u2, u3} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_4) (LinearMap.{u2, u2, max u1 u2, u3} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Pi.module.{u1, u2, u2} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap._hyg.392 : ι) => R) 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+Case conversion may be inaccurate. Consider using '#align pi_to_module.from_End_injective PiToModule.fromEnd_injectiveₓ'. -/
 theorem PiToModule.fromEnd_injective (hb : Submodule.span R (Set.range b) = ⊤) :
     Function.Injective (PiToModule.fromEnd R b) :=
   by
@@ -90,24 +124,44 @@ section
 
 variable {R} [DecidableEq ι]
 
+#print Matrix.Represents /-
 /-- We say that a matrix represents an endomorphism of `M` if the matrix acting on `ι → R` is
 equal to `f` via the projection `(ι → R) →ₗ[R] M` given by a fixed (spanning) set.  -/
 def Matrix.Represents (A : Matrix ι ι R) (f : Module.End R M) : Prop :=
   PiToModule.fromMatrix R b A = PiToModule.fromEnd R b f
 #align matrix.represents Matrix.Represents
+-/
 
 variable {b}
 
+/- warning: matrix.represents.congr_fun -> Matrix.Represents.congr_fun is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (x : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4) (fun (_x : LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Pi.Function.module.{u1, u3, u2} ι R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.{u3, u3, u3, max u1 u3, u2} R R R (ι -> R) M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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(fun (_x : LinearMap.{u3, u3, max u1 u2, max (max u1 u3) u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) 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_inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))))) => (ι -> M) -> (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4)) (LinearMap.hasCoeToFun.{u3, u3, max u1 u2, max (max u1 u3) u2} R R (ι -> M) (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (ι -> R) M (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Pi.Function.module.{u1, u3, u3} ι R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R 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(Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) x)))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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+Case conversion may be inaccurate. Consider using '#align matrix.represents.congr_fun Matrix.Represents.congr_funₓ'. -/
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   LinearMap.congr_fun h x
 #align matrix.represents.congr_fun Matrix.Represents.congr_fun
 
+/- warning: matrix.represents_iff -> Matrix.represents_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (x : ι -> R), Eq.{succ u2} M (coeFn.{max (succ (max u1 u3)) (succ u2), max (succ (max u1 u3)) (succ u2)} (LinearMap.{u3, u3, max u1 u3, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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(Semiring.toModule.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (Fintype.total.{u1, u2, u3, u3} ι M R _inst_1 (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_4 (smulCommClass_self.{u3, u2} R M (CommRing.toCommMonoid.{u3} R _inst_3) (MulActionWithZero.toMulAction.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) b) x)))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (x : ι -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : ι -> R) => M) (Matrix.mulVec.{u2, u3, u3} ι ι R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) _inst_1 A x)) (FunLike.coe.{max (max 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_inst_4 (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) b) x)))
+Case conversion may be inaccurate. Consider using '#align matrix.represents_iff Matrix.represents_iffₓ'. -/
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
   ⟨fun e x => e.congr_fun x, fun H => LinearMap.ext fun x => H x⟩
 #align matrix.represents_iff Matrix.represents_iff
 
+/- warning: matrix.represents_iff' -> Matrix.represents_iff' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (j : ι), Eq.{succ u2} M (Finset.sum.{u2, u1} M ι (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finset.univ.{u1} ι _inst_1) (fun (i : ι) => SMul.smul.{u3, u2} R M (SMulZeroClass.toHasSmul.{u3, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (SMulWithZero.toSmulZeroClass.{u3, u2} R M (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (A i j) (b i))) (coeFn.{succ u2, succ u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (fun (_x : LinearMap.{u3, u3, u2, u2} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) f (b j)))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, Iff (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) (forall (j : ι), Eq.{succ u1} M (Finset.sum.{u1, u3} M ι (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (Finset.univ.{u3} ι _inst_1) (fun (i : ι) => HSMul.hSMul.{u2, u1, u1} R M M (instHSMul.{u2, u1} R M (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (A i j) (b i))) (FunLike.coe.{succ u1, succ u1, succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) f (b j)))
+Case conversion may be inaccurate. Consider using '#align matrix.represents_iff' Matrix.represents_iff'ₓ'. -/
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) :=
   by
@@ -122,6 +176,12 @@ theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
     apply h
 #align matrix.represents_iff' Matrix.represents_iff'
 
+/- warning: matrix.represents.mul -> Matrix.Represents.mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {A' : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} {f' : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A' f') -> (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (HMul.hMul.{max u1 u3, max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u1, u1, u3} ι ι R) (instHMul.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.hasMul.{u3, u1} ι R _inst_1 (Distrib.toHasMul.{u3} R (Ring.toDistrib.{u3} R (CommRing.toRing.{u3} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toAddCommGroup.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3))))))) A A') (HMul.hMul.{u2, u2, u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (instHMul.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.End.hasMul.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)) f f'))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {A' : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} {f' : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A' f') -> (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.{u3, u3, u2} ι ι R) (Matrix.{u3, u3, u2} ι ι R) (instHMul.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.instMulMatrix.{u2, u3} ι R _inst_1 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) A A') (HMul.hMul.{u1, u1, u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHMul.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.instMulEnd.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) f f'))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.mul Matrix.Represents.mulₓ'. -/
 theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A * A').Represents b (f * f') :=
   by
@@ -133,6 +193,12 @@ theorem Matrix.Represents.mul {A A' : Matrix ι ι R} {f f' : Module.End R M} (h
   rfl
 #align matrix.represents.mul Matrix.Represents.mul
 
+/- warning: matrix.represents.one -> Matrix.Represents.one is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι], Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 1 (OfNat.mk.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 1 (One.one.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.hasOne.{u3, u1} ι R (fun (a : ι) (b : ι) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) (AddMonoidWithOne.toOne.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (AddCommGroupWithOne.toAddGroupWithOne.{u3} R (Ring.toAddCommGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_3))))))))) (OfNat.ofNat.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (OfNat.mk.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (One.one.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.module.End.hasOne.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι], Matrix.Represents.{u3, u2, u1} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) (Matrix.one.{u1, u3} ι R (fun (a : ι) (b : ι) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (OfNat.ofNat.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 1 (One.toOfNat1.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.instOneEnd.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.one Matrix.Represents.oneₓ'. -/
 theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   by
   delta Matrix.Represents PiToModule.fromMatrix
@@ -141,20 +207,44 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 :=
   rfl
 #align matrix.represents.one Matrix.Represents.one
 
+/- warning: matrix.represents.add -> Matrix.Represents.add is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {A' : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} {f' : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A' f') -> (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (HAdd.hAdd.{max u1 u3, max u1 u3, max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u1, u1, u3} ι ι R) (instHAdd.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.hasAdd.{u3, u1, u1} ι ι R (Distrib.toHasAdd.{u3} R (Ring.toDistrib.{u3} R (CommRing.toRing.{u3} R _inst_3))))) A A') (HAdd.hAdd.{u2, u2, u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (instHAdd.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.hasAdd.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))))) f f'))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {A' : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} {f' : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A' f') -> (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (HAdd.hAdd.{max u3 u2, max u3 u2, max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.{u3, u3, u2} ι ι R) (Matrix.{u3, u3, u2} ι ι R) (instHAdd.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.add.{u2, u3, u3} ι ι R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))))) A A') (HAdd.hAdd.{u1, u1, u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHAdd.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.instAddLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) f f'))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.add Matrix.Represents.addₓ'. -/
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
   delta Matrix.Represents at h h'⊢; rw [map_add, map_add, h, h']
 #align matrix.represents.add Matrix.Represents.add
 
+/- warning: matrix.represents.zero -> Matrix.Represents.zero is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u1} ι], Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 0 (OfNat.mk.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) 0 (Zero.zero.{max u1 u3} (Matrix.{u1, u1, u3} ι ι R) (Matrix.hasZero.{u3, u1, u1} ι ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_3)))))))))) (OfNat.ofNat.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 0 (OfNat.mk.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 0 (Zero.zero.{u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.hasZero.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι], Matrix.Represents.{u3, u2, u1} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) 0 (Zero.toOfNat0.{max u3 u1} (Matrix.{u3, u3, u1} ι ι R) (Matrix.zero.{u1, u3, u3} ι ι R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (OfNat.ofNat.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) 0 (Zero.toOfNat0.{u2} (Module.End.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.instZeroLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.zero Matrix.Represents.zeroₓ'. -/
 theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by delta Matrix.Represents;
   rw [map_zero, map_zero]
 #align matrix.represents.zero Matrix.Represents.zero
 
+/- warning: matrix.represents.smul -> Matrix.Represents.smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M} [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (forall (r : R), Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) (HSMul.hSMul.{u2, max u3 u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (Matrix.{u3, u3, u2} ι ι R) (instHSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (Matrix.smul.{u2, u3, u3, u2} ι ι R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) r A) (HSMul.hSMul.{u2, u1, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHSMul.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.instSMulLinearMap.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (smulCommClass_self.{u2, u1} R M (CommRing.toCommMonoid.{u2} R _inst_3) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) r f))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.smul Matrix.Represents.smulₓ'. -/
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (r : R) : (r • A).Represents b (r • f) := by delta Matrix.Represents at h⊢;
   rw [map_smul, map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
 
+/- warning: matrix.represents.eq -> Matrix.Represents.eq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] {R : Type.{u3}} [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {b : ι -> M}, (Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (forall [_inst_5 : DecidableEq.{succ u1} ι] {A : Matrix.{u1, u1, u3} ι ι R} {f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} {f' : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4}, (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u1, u2, u3} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f') -> (Eq.{succ u2} (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) f f'))
+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {b : ι -> M}, (Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (forall [_inst_5 : DecidableEq.{succ u3} ι] {A : Matrix.{u3, u3, u2} ι ι R} {f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} {f' : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4}, (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f) -> (Matrix.Represents.{u3, u1, u2} ι _inst_1 M _inst_2 R _inst_3 _inst_4 b (fun (a : ι) (b : ι) => _inst_5 a b) A f') -> (Eq.{succ u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f f'))
+Case conversion may be inaccurate. Consider using '#align matrix.represents.eq Matrix.Represents.eqₓ'. -/
 theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : A.Represents b f') : f = f' :=
   PiToModule.fromEnd_injective R b hb (h.symm.trans h')
@@ -162,6 +252,12 @@ theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A
 
 variable (b R)
 
+/- warning: matrix.is_representation -> Matrix.isRepresentation is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (ι -> M) -> (forall [_inst_5 : DecidableEq.{succ u1} ι], Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (ι -> M) -> (forall [_inst_5 : DecidableEq.{succ u1} ι], Subalgebra.{u3, max u3 u1} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => _inst_5 a b) (CommRing.toCommSemiring.{u3} R _inst_3) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3))))
+Case conversion may be inaccurate. Consider using '#align matrix.is_representation Matrix.isRepresentationₓ'. -/
 /-- The subalgebra of `matrix ι ι R` that consists of matrices that actually represent
 endomorphisms on `M`. -/
 def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
@@ -174,6 +270,12 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R)
   algebraMap_mem' r := ⟨r • 1, Matrix.Represents.one.smul r⟩
 #align matrix.is_representation Matrix.isRepresentation
 
+/- warning: matrix.is_representation.to_End -> Matrix.isRepresentation.toEnd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End Matrix.isRepresentation.toEndₓ'. -/
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
 noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b →ₐ[R] Module.End R M
     where
@@ -186,17 +288,35 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
     (r • 1 : Matrix.isRepresentation R b).2.choose_spec.Eq hb (Matrix.Represents.one.smul r)
 #align matrix.is_representation.to_End Matrix.isRepresentation.toEnd
 
+/- warning: matrix.is_representation.to_End_represents -> Matrix.isRepresentation.toEnd_represents is a dubious translation:
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_inst_3 _inst_4 b hb (fun (a : ι) (b : ι) => _inst_5 a b)) A)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_representsₓ'. -/
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :
     (A : Matrix ι ι R).Represents b (Matrix.isRepresentation.toEnd R b hb A) :=
   A.2.choose_spec
 #align matrix.is_representation.to_End_represents Matrix.isRepresentation.toEnd_represents
 
+/- warning: matrix.is_representation.eq_to_End_of_represents -> Matrix.isRepresentation.eq_toEnd_of_represents is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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+Case conversion may be inaccurate. Consider using '#align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_representsₓ'. -/
 theorem Matrix.isRepresentation.eq_toEnd_of_represents (A : Matrix.isRepresentation R b)
     {f : Module.End R M} (h : (A : Matrix ι ι R).Represents b f) :
     Matrix.isRepresentation.toEnd R b hb A = f :=
   A.2.choose_spec.Eq hb h
 #align matrix.is_representation.eq_to_End_of_represents Matrix.isRepresentation.eq_toEnd_of_represents
 
+/- warning: matrix.is_representation.to_End_exists_mem_ideal -> Matrix.isRepresentation.toEnd_exists_mem_ideal is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] (R : Type.{u3}) [_inst_3 : CommRing.{u3} R] [_inst_4 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.span.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 (Set.range.{u2, succ u1} M ι b)) (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) [_inst_5 : DecidableEq.{succ u1} ι] (f : Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))), (LE.le.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) M (Submodule.setLike.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) (LinearMap.range.{u3, u3, u2, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)))) (Module.End.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.semilinearMapClass.{u3, u3, u2, u2} R R M M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) f) (SMul.smul.{u3, u2} (Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))) (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasSMul'.{u3, u2} R M (CommRing.toCommSemiring.{u3} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) I (Top.top.{u2} (Submodule.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasTop.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)))) -> (Exists.{succ (max u1 u3)} (coeSort.{succ (max u1 u3), succ (succ (max u1 u3))} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) Type.{max u1 u3} (SetLike.hasCoeToSort.{max u1 u3, max u1 u3} (Subalgebra.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) (CommRing.toCommSemiring.{u3} R _inst_3) (Matrix.semiring.{u3, u1} ι R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_1 (fun (a : ι) (b : ι) => (fun (a : ι) (b : ι) => _inst_5 a b) a b) (CommRing.toCommSemiring.{u3} R _inst_3) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (Matrix.{u1, u1, u3} ι ι R) (Subalgebra.setLike.{u3, max u1 u3} R (Matrix.{u1, u1, u3} ι ι R) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_idealₓ'. -/
 theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I : Ideal R)
     (hI : f.range ≤ I • ⊤) : ∃ M, Matrix.isRepresentation.toEnd R b hb M = f ∧ ∀ i j, M.1 i j ∈ I :=
   by
@@ -217,6 +337,12 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
       fun i j => (bM' (b j) i).Prop⟩
 #align matrix.is_representation.to_End_exists_mem_ideal Matrix.isRepresentation.toEnd_exists_mem_ideal
 
+/- warning: matrix.is_representation.to_End_surjective -> Matrix.isRepresentation.toEnd_surjective is a dubious translation:
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+but is expected to have type
+  forall {ι : Type.{u3}} [_inst_1 : Fintype.{u3} ι] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (b : ι -> M) (hb : Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 (Set.range.{u1, succ u3} M ι b)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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+Case conversion may be inaccurate. Consider using '#align matrix.is_representation.to_End_surjective Matrix.isRepresentation.toEnd_surjectiveₓ'. -/
 theorem Matrix.isRepresentation.toEnd_surjective :
     Function.Surjective (Matrix.isRepresentation.toEnd R b hb) :=
   by
@@ -228,6 +354,12 @@ theorem Matrix.isRepresentation.toEnd_surjective :
 
 end
 
+/- warning: linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul -> LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toHasLe.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R 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(Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) f) (SMul.smul.{u2, u1} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) I (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasTop.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) -> (Exists.{succ u2} (Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (fun (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) => And (Polynomial.Monic.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p) (And (forall (k : Nat), Membership.Mem.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) R (Submodule.setLike.{u2, u2} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (Polynomial.coeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instHPow.{u2, 0} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_3) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) p) k))) (Eq.{succ u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (fun (_x : AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) => (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) -> (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) ([anonymous].{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.algebra.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 0 (OfNat.mk.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) 0 (Zero.zero.{u1} (Module.End.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.hasZero.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] (R : Type.{u2}) [_inst_3 : CommRing.{u2} R] [_inst_4 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.Finite.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4] (f : Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))), (LE.le.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.completeLattice.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))))) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) f) (HSMul.hSMul.{u2, u1, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (instHSMul.{u2, u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.hasSMul'.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) I (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) -> (Exists.{succ u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (fun (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => And (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) p) (And (forall (k : Nat), Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Semiring.toNonAssocSemiring.{u1} (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))) (Algebra.toModule.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)))))) (Polynomial.aeval.{u2, u1} R (Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (CommRing.toCommSemiring.{u2} R _inst_3) (Module.End.semiring.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) f) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) => Module.End.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) p) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 _inst_4 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)))))))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smulₓ'. -/
 /-- The **Cayley-Hamilton Theorem** for f.g. modules over arbitrary rings states that for each
 `R`-endomorphism `φ` of an `R`-module `M` such that `φ(M) ≤ I • M` for some ideal `I`, there
 exists some `n` and some `aᵢ ∈ Iⁱ` such that `φⁿ + a₁ φⁿ⁻¹ + ⋯ + aₙ = 0`.
@@ -256,9 +388,11 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
     · infer_instance
 #align linear_map.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul
 
+#print LinearMap.exists_monic_and_aeval_eq_zero /-
 theorem LinearMap.exists_monic_and_aeval_eq_zero [Module.Finite R M] (f : Module.End R M) :
     ∃ p : R[X], p.Monic ∧ Polynomial.aeval f p = 0 :=
   (LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul R f ⊤ (by simp)).imp
     fun p h => h.imp_right And.right
 #align linear_map.exists_monic_and_aeval_eq_zero LinearMap.exists_monic_and_aeval_eq_zero
+-/

62c0a4ef

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

62c0a4ef

feat: MulActionHom in the semilinear style (#6057)

Generalize MulActionHom so that it allows two different monoids acting, related by a morphism. This is inspired by the treatment of (semi)linear maps in mathlib, and allows to refactor them.

Let M, N, X, Y be types, with SMul M X and SMul N Y, and let φ : M → N be a map.

MulActionHom φ X Y, the type of equivariant functions from X to Y, consists of functions f : X → Y such that f (m • x) = (φ m) • (f x) for all m : M and x : X.

Assume that we have Monoid M, Monoid N and that φ : M →* N. For A, B by types with AddMonoid A and AddMonoid B, endowed with DistribMulAction M A and DistribMulAction M B:

DistribMulActionHom φ A B is the type of equivariant additive monoid homomorphisms from A to B.

Similarly, when R and S are types with Semiring R, Semiring S, MulSemiringAction M R and MulSemiringAction N S

SMulSemiringHom φ R S is the type of equivariant ring homomorphisms from R to S.

The above types have corresponding classes:

MulActionHomClass F φ X Y states that F is a type of bundled X → Y homs which are φ-equivariant
DistribMulActionHomClass F φ A B states that F is a type of bundled A → B homs preserving the additive monoid structure and φ-equivariant
SMulSemiringHomClass F φ R S states that F is a type of bundled R → S homs preserving the ring structure and φ-equivariant

Notation

We introduce the following notation to code equivariant maps (the subscript index ₑ is for equivariant) :

X →ₑ[φ] Y is MulActionHom φ X Y.
A →ₑ+[φ] B is DistribMulActionHom φ A B.
R →ₑ+*[φ] S is MulSemiringActionHom φ R S.

When M = N and φ = MonoidHom.id M, we provide the backward compatible notation :

X →[M] Y is MulActionHom ([@id](https://github.com/id) M) X Y
A →+[M] B is DistribMulActionHom (MonoidHom.id M) A B
R →+*[M] S is MulSemiringActionHom (MonoidHom.id M) R S

This more general definition is propagated all over mathlib, in particular to LinearMap.

The treatment of composition of equivariant maps is inspired by that of semilinear maps. We provide classes CompTriple and MonoidHom.CompTriple of “composable triples`, and various instances for them.

8b50609c

Diff

@@ -141,7 +141,7 @@ theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by
 theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
     (r : R) : (r • A).Represents b (r • f) := by
   delta Matrix.Represents at h ⊢
-  rw [SMulHomClass.map_smul, SMulHomClass.map_smul, h]
+  rw [_root_.map_smul, _root_.map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
 
 theorem Matrix.Represents.algebraMap (r : R) :

62c0a4ef

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -24,9 +24,7 @@ This is used to conclude the Cayley-Hamilton theorem for f.g. modules over arbit
 
 
 variable {ι : Type*} [Fintype ι]
-
 variable {M : Type*} [AddCommGroup M] (R : Type*) [CommRing R] [Module R M] (I : Ideal R)
-
 variable (b : ι → M) (hb : Submodule.span R (Set.range b) = ⊤)
 
 open BigOperators Polynomial Matrix

62c0a4ef

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -201,7 +201,7 @@ theorem Matrix.isRepresentation.toEnd_exists_mem_ideal (f : Module.End R M) (I :
   let A : Matrix ι ι R := fun i j => bM' (b j) i
   have : A.Represents b f := by
     rw [Matrix.represents_iff']
-    dsimp
+    dsimp [A]
     intro j
     specialize hbM' (b j)
     rwa [Ideal.finsuppTotal_apply_eq_of_fintype] at hbM'

62c0a4ef

chore: Matrix.mulVec and Matrix.vecMul get infix notation (#10297)

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>

deb48fab

Diff

@@ -29,7 +29,7 @@ variable {M : Type*} [AddCommGroup M] (R : Type*) [CommRing R] [Module R M] (I :
 
 variable (b : ι → M) (hb : Submodule.span R (Set.range b) = ⊤)
 
-open BigOperators Polynomial
+open BigOperators Polynomial Matrix
 
 /-- The composition of a matrix (as an endomorphism of `ι → R`) with the projection
 `(ι → R) →ₗ[R] M`.  -/
@@ -38,7 +38,7 @@ def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R)
 #align pi_to_module.from_matrix PiToModule.fromMatrix
 
 theorem PiToModule.fromMatrix_apply [DecidableEq ι] (A : Matrix ι ι R) (w : ι → R) :
-    PiToModule.fromMatrix R b A w = Fintype.total R R b (A.mulVec w) :=
+    PiToModule.fromMatrix R b A w = Fintype.total R R b (A *ᵥ w) :=
   rfl
 #align pi_to_module.from_matrix_apply PiToModule.fromMatrix_apply
 
@@ -90,12 +90,12 @@ def Matrix.Represents (A : Matrix ι ι R) (f : Module.End R M) : Prop :=
 variable {b}
 
 theorem Matrix.Represents.congr_fun {A : Matrix ι ι R} {f : Module.End R M} (h : A.Represents b f)
-    (x) : Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
+    (x) : Fintype.total R R b (A *ᵥ x) = f (Fintype.total R R b x) :=
   LinearMap.congr_fun h x
 #align matrix.represents.congr_fun Matrix.Represents.congr_fun
 
 theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
-    A.Represents b f ↔ ∀ x, Fintype.total R R b (A.mulVec x) = f (Fintype.total R R b x) :=
+    A.Represents b f ↔ ∀ x, Fintype.total R R b (A *ᵥ x) = f (Fintype.total R R b x) :=
   ⟨fun e x => e.congr_fun x, fun H => LinearMap.ext fun x => H x⟩
 #align matrix.represents_iff Matrix.represents_iff

62c0a4ef

refactor(Data/Matrix/Basic): use a defeq for scalar that matches its docstring (#8115)

This changes the defeq from scalar a = a • 1 to scalar a = diagonal fun _ => a, which has the nice bonus of making algebraMap_eq_diagonal true by rfl.

As a result, we need a new smul_one_eq_diagonal lemma to rewrite diagonal fun _ => a back into a • 1, along with some variants for convenience.

In the long term we could generalize this to non-unital rings, now that it needs no 1.

4b30f25b

Diff

@@ -146,6 +146,10 @@ theorem Matrix.Represents.smul {A : Matrix ι ι R} {f : Module.End R M} (h : A.
   rw [SMulHomClass.map_smul, SMulHomClass.map_smul, h]
 #align matrix.represents.smul Matrix.Represents.smul
 
+theorem Matrix.Represents.algebraMap (r : R) :
+    (algebraMap _ (Matrix ι ι R) r).Represents b (algebraMap _ (Module.End R M) r) := by
+  simpa only [Algebra.algebraMap_eq_smul_one] using Matrix.Represents.one.smul r
+
 theorem Matrix.Represents.eq {A : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : A.Represents b f') : f = f' :=
   PiToModule.fromEnd_injective R b hb (h.symm.trans h')
@@ -161,7 +165,7 @@ def Matrix.isRepresentation : Subalgebra R (Matrix ι ι R) where
   one_mem' := ⟨1, Matrix.Represents.one⟩
   add_mem' := fun ⟨f₁, e₁⟩ ⟨f₂, e₂⟩ => ⟨f₁ + f₂, e₁.add e₂⟩
   zero_mem' := ⟨0, Matrix.Represents.zero⟩
-  algebraMap_mem' r := ⟨r • (1 : Module.End R M), Matrix.Represents.one.smul r⟩
+  algebraMap_mem' r := ⟨algebraMap _ _ r, .algebraMap _⟩
 #align matrix.is_representation Matrix.isRepresentation
 
 /-- The map sending a matrix to the endomorphism it represents. This is an `R`-algebra morphism. -/
@@ -173,7 +177,7 @@ noncomputable def Matrix.isRepresentation.toEnd : Matrix.isRepresentation R b 
   map_zero' := (0 : Matrix.isRepresentation R b).2.choose_spec.eq hb Matrix.Represents.zero
   map_add' A₁ A₂ := (A₁ + A₂).2.choose_spec.eq hb (A₁.2.choose_spec.add A₂.2.choose_spec)
   commutes' r :=
-    (r • (1 : Matrix.isRepresentation R b)).2.choose_spec.eq hb (Matrix.Represents.one.smul r)
+    (algebraMap _ (Matrix.isRepresentation R b) r).2.choose_spec.eq hb (.algebraMap r)
 #align matrix.is_representation.to_End Matrix.isRepresentation.toEnd
 
 theorem Matrix.isRepresentation.toEnd_represents (A : Matrix.isRepresentation R b) :

62c0a4ef

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -23,9 +23,9 @@ This is used to conclude the Cayley-Hamilton theorem for f.g. modules over arbit
 -/
 
 
-variable {ι : Type _} [Fintype ι]
+variable {ι : Type*} [Fintype ι]
 
-variable {M : Type _} [AddCommGroup M] (R : Type _) [CommRing R] [Module R M] (I : Ideal R)
+variable {M : Type*} [AddCommGroup M] (R : Type*) [CommRing R] [Module R M] (I : Ideal R)
 
 variable (b : ι → M) (hb : Submodule.span R (Set.range b) = ⊤)

62c0a4ef

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -12,7 +12,7 @@ import Mathlib.LinearAlgebra.Matrix.ToLin
 
 # Cayley-Hamilton theorem for f.g. modules.
 
-Given a fixed finite spanning set `b : ι → M` of a `R`-module `M`, we say that a matrix `M`
+Given a fixed finite spanning set `b : ι → M` of an `R`-module `M`, we say that a matrix `M`
 represents an endomorphism `f : M →ₗ[R] M` if the matrix as an endomorphism of `ι → R` commutes
 with `f` via the projection `(ι → R) →ₗ[R] M` given by `b`.

62c0a4ef

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.linear_map
-! leanprover-community/mathlib commit 62c0a4ef1441edb463095ea02a06e87f3dfe135c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
 import Mathlib.LinearAlgebra.Matrix.ToLin
 
+#align_import linear_algebra.matrix.charpoly.linear_map from "leanprover-community/mathlib"@"62c0a4ef1441edb463095ea02a06e87f3dfe135c"
+
 /-!
 
 # Cayley-Hamilton theorem for f.g. modules.

62c0a4ef

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -231,7 +231,8 @@ theorem LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_s
   classical
     cases subsingleton_or_nontrivial R
     · exact ⟨0, Polynomial.monic_of_subsingleton _, by simp⟩
-    obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ := Module.Finite.out
+    obtain ⟨s : Finset M, hs : Submodule.span R (s : Set M) = ⊤⟩ :=
+      Module.Finite.out (R := R) (M := M)
     -- Porting note: `H` was `rfl`
     obtain ⟨A, H, h⟩ :=
       Matrix.isRepresentation.toEnd_exists_mem_ideal R ((↑) : s → M)

62c0a4ef

fix: ∑' precedence (#5615)

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

03fc68aa

Diff

@@ -103,7 +103,7 @@ theorem Matrix.represents_iff {A : Matrix ι ι R} {f : Module.End R M} :
 #align matrix.represents_iff Matrix.represents_iff
 
 theorem Matrix.represents_iff' {A : Matrix ι ι R} {f : Module.End R M} :
-    A.Represents b f ↔ ∀ j, (∑ i : ι, A i j • b i) = f (b j) := by
+    A.Represents b f ↔ ∀ j, ∑ i : ι, A i j • b i = f (b j) := by
   constructor
   · intro h i
     have := LinearMap.congr_fun h (Pi.single i 1)

62c0a4ef

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -135,7 +135,7 @@ theorem Matrix.Represents.one : (1 : Matrix ι ι R).Represents b 1 := by
 
 theorem Matrix.Represents.add {A A' : Matrix ι ι R} {f f' : Module.End R M} (h : A.Represents b f)
     (h' : Matrix.Represents b A' f') : (A + A').Represents b (f + f') := by
-  delta Matrix.Represents at h h'⊢; rw [map_add, map_add, h, h']
+  delta Matrix.Represents at h h' ⊢; rw [map_add, map_add, h, h']
 #align matrix.represents.add Matrix.Represents.add
 
 theorem Matrix.Represents.zero : (0 : Matrix ι ι R).Represents b 0 := by

62c0a4ef

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -13,7 +13,7 @@ import Mathlib.LinearAlgebra.Matrix.ToLin
 
 /-!
 
-# Calyley-Hamilton theorem for f.g. modules.
+# Cayley-Hamilton theorem for f.g. modules.
 
 Given a fixed finite spanning set `b : ι → M` of a `R`-module `M`, we say that a matrix `M`
 represents an endomorphism `f : M →ₗ[R] M` if the matrix as an endomorphism of `ι → R` commutes
@@ -34,7 +34,7 @@ variable (b : ι → M) (hb : Submodule.span R (Set.range b) = ⊤)
 
 open BigOperators Polynomial
 
-/-- The composition of a matrix (as an endomporphism of `ι → R`) with the projection
+/-- The composition of a matrix (as an endomorphism of `ι → R`) with the projection
 `(ι → R) →ₗ[R] M`.  -/
 def PiToModule.fromMatrix [DecidableEq ι] : Matrix ι ι R →ₗ[R] (ι → R) →ₗ[R] M :=
   (LinearMap.llcomp R _ _ _ (Fintype.total R R b)).comp algEquivMatrix'.symm.toLinearMap

62c0a4ef

feat: port LinearAlgebra.Matrix.Charpoly.LinearMap (#4172)

b37b871d

`linear_algebra.matrix.charpoly.linear_map` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Notation

Dependencies 10 + 619

linear_algebra.matrix.charpoly.linear_map ⟷ Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Notation

Dependencies 10 + 619

`linear_algebra.matrix.charpoly.linear_map` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap`