linear_algebra.eigenspace.minpoly ⟷ Mathlib.LinearAlgebra.Eigenspace.Minpoly

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

@@ -64,7 +64,7 @@ theorem aeval_apply_of_hasEigenvector {f : End K V} {p : K[X]} {μ : K} {x : V}
   · intro a; simp [Module.algebraMap_end_apply]
   · intro p q hp hq; simp [hp, hq, add_smul]
   · intro n a hna
-    rw [mul_comm, pow_succ, mul_assoc, AlgHom.map_mul, LinearMap.mul_apply, mul_comm, hna]
+    rw [mul_comm, pow_succ', mul_assoc, AlgHom.map_mul, LinearMap.mul_apply, mul_comm, hna]
     simp only [mem_eigenspace_iff.1 h.1, smul_smul, aeval_X, eval_mul, eval_C, eval_pow, eval_X,
       LinearMap.map_smulₛₗ, RingHom.id_apply, mul_comm]
 #align module.End.aeval_apply_of_has_eigenvector Module.End.aeval_apply_of_hasEigenvector

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

@@ -38,8 +38,7 @@ theorem eigenspace_aeval_polynomial_degree_1 (f : End K V) (q : K[X]) (hq : degr
   calc
     eigenspace f (-q.coeff 0 / q.leadingCoeff) =
         (q.leadingCoeff • f - algebraMap K (End K V) (-q.coeff 0)).ker :=
-      by rw [eigenspace_div]; intro h; rw [leading_coeff_eq_zero_iff_deg_eq_bot.1 h] at hq ;
-      cases hq
+      by rw [eigenspace_div]; intro h; rw [leading_coeff_eq_zero_iff_deg_eq_bot.1 h] at hq; cases hq
     _ = (aeval f (C q.leadingCoeff * X + C (q.coeff 0))).ker := by rw [C_mul', aeval_def];
       simp [algebraMap, Algebra.toRingHom]
     _ = (aeval f q).ker := by rwa [← eq_X_add_C_of_degree_eq_one]
@@ -97,8 +96,8 @@ theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue
     apply minpoly.ne_zero f.is_integral
     rw [hp, Con, MulZeroClass.mul_zero]
   have h_deg := minpoly.degree_le_of_ne_zero K f p_ne_0 _
-  · rw [hp, degree_mul, degree_X_sub_C, Polynomial.degree_eq_natDegree p_ne_0] at h_deg 
-    norm_cast at h_deg 
+  · rw [hp, degree_mul, degree_X_sub_C, Polynomial.degree_eq_natDegree p_ne_0] at h_deg
+    norm_cast at h_deg
     linarith
   · have h_aeval := minpoly.aeval K f
     revert h_aeval

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

@@ -120,7 +120,8 @@ noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
       have h : minpoly K f ≠ 0 := minpoly.ne_zero f.is_integral
       convert (minpoly K f).rootSet_finite K using 1
       ext μ
-      classical
+      classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← has_eigenvalue_iff_is_root,
+        has_eigenvalue]
 
 end End
 

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

@@ -120,8 +120,7 @@ noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
       have h : minpoly K f ≠ 0 := minpoly.ne_zero f.is_integral
       convert (minpoly K f).rootSet_finite K using 1
       ext μ
-      classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← has_eigenvalue_iff_is_root,
-        has_eigenvalue]
+      classical
 
 end End
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 -/
-import Mathbin.LinearAlgebra.Eigenspace.Basic
-import Mathbin.FieldTheory.Minpoly.Field
+import LinearAlgebra.Eigenspace.Basic
+import FieldTheory.Minpoly.Field
 
 #align_import linear_algebra.eigenspace.minpoly from "leanprover-community/mathlib"@"c3216069e5f9369e6be586ccbfcde2592b3cec92"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
-
-! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit c3216069e5f9369e6be586ccbfcde2592b3cec92
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Eigenspace.Basic
 import Mathbin.FieldTheory.Minpoly.Field
 
+#align_import linear_algebra.eigenspace.minpoly from "leanprover-community/mathlib"@"c3216069e5f9369e6be586ccbfcde2592b3cec92"
+
 /-!
 # Eigenvalues are the roots of the minimal polynomial.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
+! leanprover-community/mathlib commit c3216069e5f9369e6be586ccbfcde2592b3cec92
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -117,15 +117,14 @@ theorem hasEigenvalue_iff_isRoot : f.HasEigenvalue μ ↔ (minpoly K f).IsRoot 
 
 /-- An endomorphism of a finite-dimensional vector space has finitely many eigenvalues. -/
 noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
-  Set.Finite.fintype
-    (by
+  Set.Finite.fintype <|
+    show {μ | eigenspace f μ ≠ ⊥}.Finite
+      by
       have h : minpoly K f ≠ 0 := minpoly.ne_zero f.is_integral
-      convert (minpoly K f).rootSet_finite K
+      convert (minpoly K f).rootSet_finite K using 1
       ext μ
-      have : μ ∈ {μ : K | f.eigenspace μ = ⊥ → False} ↔ ¬f.eigenspace μ = ⊥ := by tauto
-      convert rfl.mpr this
       classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← has_eigenvalue_iff_is_root,
-        has_eigenvalue])
+        has_eigenvalue]
 
 end End
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit 6b0169218d01f2837d79ea2784882009a0da1aa1
+! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.FieldTheory.Minpoly.Field
 /-!
 # Eigenvalues are the roots of the minimal polynomial.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Tags
 
 eigenvalue, minimal polynomial
@@ -121,7 +124,7 @@ noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
       ext μ
       have : μ ∈ {μ : K | f.eigenspace μ = ⊥ → False} ↔ ¬f.eigenspace μ = ⊥ := by tauto
       convert rfl.mpr this
-      simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← has_eigenvalue_iff_is_root,
+      classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← has_eigenvalue_iff_is_root,
         has_eigenvalue])
 
 end End

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

@@ -32,6 +32,7 @@ open scoped Polynomial
 
 variable {K : Type v} {V : Type w} [Field K] [AddCommGroup V] [Module K V]
 
+#print Module.End.eigenspace_aeval_polynomial_degree_1 /-
 theorem eigenspace_aeval_polynomial_degree_1 (f : End K V) (q : K[X]) (hq : degree q = 1) :
     eigenspace f (-q.coeff 0 / q.leadingCoeff) = (aeval f q).ker :=
   calc
@@ -43,7 +44,9 @@ theorem eigenspace_aeval_polynomial_degree_1 (f : End K V) (q : K[X]) (hq : degr
       simp [algebraMap, Algebra.toRingHom]
     _ = (aeval f q).ker := by rwa [← eq_X_add_C_of_degree_eq_one]
 #align module.End.eigenspace_aeval_polynomial_degree_1 Module.End.eigenspace_aeval_polynomial_degree_1
+-/
 
+#print Module.End.ker_aeval_ring_hom'_unit_polynomial /-
 theorem ker_aeval_ring_hom'_unit_polynomial (f : End K V) (c : K[X]ˣ) :
     (aeval f (c : K[X])).ker = ⊥ :=
   by
@@ -52,7 +55,9 @@ theorem ker_aeval_ring_hom'_unit_polynomial (f : End K V) (c : K[X]ˣ) :
   apply ker_algebra_map_End
   apply coeff_coe_units_zero_ne_zero c
 #align module.End.ker_aeval_ring_hom'_unit_polynomial Module.End.ker_aeval_ring_hom'_unit_polynomial
+-/
 
+#print Module.End.aeval_apply_of_hasEigenvector /-
 theorem aeval_apply_of_hasEigenvector {f : End K V} {p : K[X]} {μ : K} {x : V}
     (h : f.HasEigenvector μ x) : aeval f p x = p.eval μ • x :=
   by
@@ -64,7 +69,9 @@ theorem aeval_apply_of_hasEigenvector {f : End K V} {p : K[X]} {μ : K} {x : V}
     simp only [mem_eigenspace_iff.1 h.1, smul_smul, aeval_X, eval_mul, eval_C, eval_pow, eval_X,
       LinearMap.map_smulₛₗ, RingHom.id_apply, mul_comm]
 #align module.End.aeval_apply_of_has_eigenvector Module.End.aeval_apply_of_hasEigenvector
+-/
 
+#print Module.End.isRoot_of_hasEigenvalue /-
 theorem isRoot_of_hasEigenvalue {f : End K V} {μ : K} (h : f.HasEigenvalue μ) :
     (minpoly K f).IsRoot μ :=
   by
@@ -72,11 +79,13 @@ theorem isRoot_of_hasEigenvalue {f : End K V} {μ : K} (h : f.HasEigenvalue μ)
   refine' Or.resolve_right (smul_eq_zero.1 _) ne0
   simp [← aeval_apply_of_has_eigenvector ⟨H, ne0⟩, minpoly.aeval K f]
 #align module.End.is_root_of_has_eigenvalue Module.End.isRoot_of_hasEigenvalue
+-/
 
 variable [FiniteDimensional K V] (f : End K V)
 
 variable {f} {μ : K}
 
+#print Module.End.hasEigenvalue_of_isRoot /-
 theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue μ :=
   by
   cases' dvd_iff_is_root.2 h with p hp
@@ -95,10 +104,13 @@ theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue
     revert h_aeval
     simp [hp, ← hu]
 #align module.End.has_eigenvalue_of_is_root Module.End.hasEigenvalue_of_isRoot
+-/
 
+#print Module.End.hasEigenvalue_iff_isRoot /-
 theorem hasEigenvalue_iff_isRoot : f.HasEigenvalue μ ↔ (minpoly K f).IsRoot μ :=
   ⟨isRoot_of_hasEigenvalue, hasEigenvalue_of_isRoot⟩
 #align module.End.has_eigenvalue_iff_is_root Module.End.hasEigenvalue_iff_isRoot
+-/
 
 /-- An endomorphism of a finite-dimensional vector space has finitely many eigenvalues. -/
 noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=

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

@@ -42,7 +42,6 @@ theorem eigenspace_aeval_polynomial_degree_1 (f : End K V) (q : K[X]) (hq : degr
     _ = (aeval f (C q.leadingCoeff * X + C (q.coeff 0))).ker := by rw [C_mul', aeval_def];
       simp [algebraMap, Algebra.toRingHom]
     _ = (aeval f q).ker := by rwa [← eq_X_add_C_of_degree_eq_one]
-    
 #align module.End.eigenspace_aeval_polynomial_degree_1 Module.End.eigenspace_aeval_polynomial_degree_1
 
 theorem ker_aeval_ring_hom'_unit_polynomial (f : End K V) (c : K[X]ˣ) :

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

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -57,7 +57,7 @@ theorem aeval_apply_of_hasEigenvector {f : End K V} {p : K[X]} {μ : K} {x : V}
   · intro a; simp [Module.algebraMap_end_apply]
   · intro p q hp hq; simp [hp, hq, add_smul]
   · intro n a hna
-    rw [mul_comm, pow_succ, mul_assoc, AlgHom.map_mul, LinearMap.mul_apply, mul_comm, hna]
+    rw [mul_comm, pow_succ', mul_assoc, AlgHom.map_mul, LinearMap.mul_apply, mul_comm, hna]
     simp only [mem_eigenspace_iff.1 h.1, smul_smul, aeval_X, eval_mul, eval_C, eval_pow, eval_X,
       LinearMap.map_smulₛₗ, RingHom.id_apply, mul_comm]
 #align module.End.aeval_apply_of_has_eigenvector Module.End.aeval_apply_of_hasEigenvector

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -70,7 +70,6 @@ theorem isRoot_of_hasEigenvalue {f : End K V} {μ : K} (h : f.HasEigenvalue μ)
 #align module.End.is_root_of_has_eigenvalue Module.End.isRoot_of_hasEigenvalue
 
 variable [FiniteDimensional K V] (f : End K V)
-
 variable {f} {μ : K}
 
 theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue μ := by

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -89,7 +89,7 @@ theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue
   have h_deg := minpoly.degree_le_of_ne_zero K f p_ne_0 this
   rw [hp, degree_mul, degree_X_sub_C, Polynomial.degree_eq_natDegree p_ne_0] at h_deg
   norm_cast at h_deg
-  linarith
+  omega
 #align module.End.has_eigenvalue_of_is_root Module.End.hasEigenvalue_of_isRoot
 
 theorem hasEigenvalue_iff_isRoot : f.HasEigenvalue μ ↔ (minpoly K f).IsRoot μ :=

The main change is to upgrade the existing Module.End.eigenspaces_independent, which applied only to eigenspaces (and required a [Field K] assumption) to Module.End.independent_generalizedEigenspace, which applies to generalized eigenspaces (and requires only [NoZeroSMulDivisors R M])

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>

@@ -96,19 +96,18 @@ theorem hasEigenvalue_iff_isRoot : f.HasEigenvalue μ ↔ (minpoly K f).IsRoot 
   ⟨isRoot_of_hasEigenvalue, hasEigenvalue_of_isRoot⟩
 #align module.End.has_eigenvalue_iff_is_root Module.End.hasEigenvalue_iff_isRoot
 
+variable (f)
+
+lemma finite_hasEigenvalue : Set.Finite f.HasEigenvalue := by
+  have h : minpoly K f ≠ 0 := minpoly.ne_zero f.isIntegral
+  convert (minpoly K f).rootSet_finite K
+  ext μ
+  change f.HasEigenvalue μ ↔ _
+  rw [hasEigenvalue_iff_isRoot, mem_rootSet_of_ne h, IsRoot, coe_aeval_eq_eval]
+
 /-- An endomorphism of a finite-dimensional vector space has finitely many eigenvalues. -/
-noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
-  Set.Finite.fintype <| show {μ | eigenspace f μ ≠ ⊥}.Finite by
-    have h : minpoly K f ≠ 0 := minpoly.ne_zero f.isIntegral
-    convert (minpoly K f).rootSet_finite K
-    ext μ
-    -- Porting note: was the below, but this applied unwanted simp lemmas
-    -- ```
-    -- classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← hasEigenvalue_iff_isRoot,
-    --   HasEigenvalue]
-    -- ```
-    rw [Set.mem_setOf_eq, ← HasEigenvalue, hasEigenvalue_iff_isRoot, mem_rootSet_of_ne h, IsRoot,
-      coe_aeval_eq_eval]
+noncomputable instance : Fintype f.Eigenvalues :=
+  Set.Finite.fintype f.finite_hasEigenvalue
 
 end End
 

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -64,7 +64,7 @@ theorem aeval_apply_of_hasEigenvector {f : End K V} {p : K[X]} {μ : K} {x : V}
 
 theorem isRoot_of_hasEigenvalue {f : End K V} {μ : K} (h : f.HasEigenvalue μ) :
     (minpoly K f).IsRoot μ := by
-  rcases(Submodule.ne_bot_iff _).1 h with ⟨w, ⟨H, ne0⟩⟩
+  rcases (Submodule.ne_bot_iff _).1 h with ⟨w, ⟨H, ne0⟩⟩
   refine' Or.resolve_right (smul_eq_zero.1 _) ne0
   simp [← aeval_apply_of_hasEigenvector ⟨H, ne0⟩, minpoly.aeval K f]
 #align module.End.is_root_of_has_eigenvalue Module.End.isRoot_of_hasEigenvalue

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -81,7 +81,7 @@ theorem hasEigenvalue_of_isRoot (h : (minpoly K f).IsRoot μ) : f.HasEigenvalue
   have p_ne_0 : p ≠ 0 := by
     intro con
     apply minpoly.ne_zero f.isIntegral
-    rw [hp, con, MulZeroClass.mul_zero]
+    rw [hp, con, mul_zero]
   have : (aeval f) p = 0 := by
     have h_aeval := minpoly.aeval K f
     revert h_aeval

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
-
-! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit c3216069e5f9369e6be586ccbfcde2592b3cec92
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Eigenspace.Basic
 import Mathlib.FieldTheory.Minpoly.Field
 
+#align_import linear_algebra.eigenspace.minpoly from "leanprover-community/mathlib"@"c3216069e5f9369e6be586ccbfcde2592b3cec92"
+
 /-!
 # Eigenvalues are the roots of the minimal polynomial.
 

This was already ported in #5254

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
+! leanprover-community/mathlib commit c3216069e5f9369e6be586ccbfcde2592b3cec92
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

This removes most of a scary porting note that is no longer true.

@@ -101,25 +101,17 @@ theorem hasEigenvalue_iff_isRoot : f.HasEigenvalue μ ↔ (minpoly K f).IsRoot 
 
 /-- An endomorphism of a finite-dimensional vector space has finitely many eigenvalues. -/
 noncomputable instance (f : End K V) : Fintype f.Eigenvalues :=
-  -- Porting note: added `show` to avoid unfolding `Set K` to `K → Prop`
-  show Fintype { μ : K | f.HasEigenvalue μ } from
-  Set.Finite.fintype
-    (by
-      have h : minpoly K f ≠ 0 := minpoly.ne_zero f.isIntegral
-      convert (minpoly K f).rootSet_finite K
-      ext μ
-      -- Porting note: was
-      -- have : μ ∈ {μ : K | f.eigenspace μ = ⊥ → False} ↔ ¬f.eigenspace μ = ⊥ := by tauto
-      -- convert rfl.mpr this
-      -- simp only [Polynomial.rootSet_def, Polynomial.mem_roots h, ← hasEigenvalue_iff_isRoot,
-      --   HasEigenvalue]
-      -- which didn't work, but worked with
-      -- simp only [Polynomial.rootSet_def, Polynomial.mem_roots h, ← hasEigenvalue_iff_isRoot,
-      --   HasEigenvalue, (Multiset.mem_toFinset), Algebra.id.map_eq_id, iff_self, Ne.def,
-      --   Polynomial.map_id, Finset.mem_coe]
-      -- but the code below is simpler.
-      rw [Set.mem_setOf_eq, hasEigenvalue_iff_isRoot, mem_rootSet_of_ne h, IsRoot,
-        coe_aeval_eq_eval])
+  Set.Finite.fintype <| show {μ | eigenspace f μ ≠ ⊥}.Finite by
+    have h : minpoly K f ≠ 0 := minpoly.ne_zero f.isIntegral
+    convert (minpoly K f).rootSet_finite K
+    ext μ
+    -- Porting note: was the below, but this applied unwanted simp lemmas
+    -- ```
+    -- classical simp [Polynomial.rootSet_def, Polynomial.mem_roots h, ← hasEigenvalue_iff_isRoot,
+    --   HasEigenvalue]
+    -- ```
+    rw [Set.mem_setOf_eq, ← HasEigenvalue, hasEigenvalue_iff_isRoot, mem_rootSet_of_ne h, IsRoot,
+      coe_aeval_eq_eval]
 
 end End
 

The important thing to forward-port here is the addition of [DecidableEq _] to a handful of lemmas.

linear_algebra.eigenspace.minpoly did not need anything forward-porting, as the proof which broke in mathlib3 did not break in mathlib4.

The nthRootsFinset_def lemma was forgotten in the mathlib3 PR.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp
 
 ! This file was ported from Lean 3 source module linear_algebra.eigenspace.minpoly
-! leanprover-community/mathlib commit 6b0169218d01f2837d79ea2784882009a0da1aa1
+! leanprover-community/mathlib commit 8efcf8022aac8e01df8d302dcebdbc25d6a886c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Moritz Firsching <firsching@google.com>