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

@@ -61,10 +61,10 @@ theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A} (hp
     (h : ¬IsUnit (aeval a (Multiset.map (fun x : R => X - C x) p.roots).Prod)) :
     ∃ k : R, k ∈ σ a ∧ eval k p = 0 :=
   by
-  rw [← Multiset.prod_toList, AlgHom.map_list_prod] at h 
+  rw [← Multiset.prod_toList, AlgHom.map_list_prod] at h
   replace h := mt List.prod_isUnit h
   simp only [Classical.not_forall, exists_prop, aeval_C, Multiset.mem_toList, List.mem_map, aeval_X,
-    exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h 
+    exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h
   rcases h with ⟨r, r_mem, r_nu⟩
   exact ⟨r, by rwa [mem_iff, ← IsUnit.sub_iff], by rwa [← is_root.def, ← mem_roots hp]⟩
 #align spectrum.exists_mem_of_not_is_unit_aeval_prod spectrum.exists_mem_of_not_isUnit_aeval_prodₓ
@@ -92,7 +92,7 @@ theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (fun k => eval k p) '' 
   rintro _ ⟨k, hk, rfl⟩
   let q := C (eval k p) - p
   have hroot : is_root q k := by simp only [eval_C, eval_sub, sub_self, is_root.def]
-  rw [← mul_div_eq_iff_is_root, ← neg_mul_neg, neg_sub] at hroot 
+  rw [← mul_div_eq_iff_is_root, ← neg_mul_neg, neg_sub] at hroot
   have aeval_q_eq : ↑ₐ (eval k p) - aeval a p = aeval a q := by
     simp only [aeval_C, AlgHom.map_sub, sub_left_inj]
   rw [mem_iff, aeval_q_eq, ← hroot, aeval_mul]
@@ -123,7 +123,7 @@ theorem map_polynomial_aeval_of_degree_pos [IsAlgClosed 𝕜] (a : A) (p : 𝕜[
   have p_a_eq : aeval a (C k - p) = ↑ₐ k - aeval a p := by
     simp only [aeval_C, AlgHom.map_sub, sub_left_inj]
   rw [mem_iff, ← p_a_eq, hprod, aeval_mul, ((Commute.all _ _).map (aeval a)).isUnit_mul_iff,
-    aeval_C] at hk 
+    aeval_C] at hk
   replace hk := exists_mem_of_not_is_unit_aeval_prod h_ne (not_and.mp hk lead_unit)
   rcases hk with ⟨r, r_mem, r_ev⟩
   exact ⟨r, r_mem, symm (by simpa [eval_sub, eval_C, sub_eq_zero] using r_ev)⟩
@@ -179,8 +179,8 @@ theorem nonempty_of_isAlgClosed_of_finiteDimensional [IsAlgClosed 𝕜] [Nontriv
     [I : FiniteDimensional 𝕜 A] (a : A) : (σ a).Nonempty :=
   by
   obtain ⟨p, ⟨h_mon, h_eval_p⟩⟩ := isIntegral_of_noetherian (IsNoetherian.iff_fg.2 I) a
-  have nu : ¬IsUnit (aeval a p) := by rw [← aeval_def] at h_eval_p ; rw [h_eval_p]; simp
-  rw [eq_prod_roots_of_monic_of_splits_id h_mon (IsAlgClosed.splits p)] at nu 
+  have nu : ¬IsUnit (aeval a p) := by rw [← aeval_def] at h_eval_p; rw [h_eval_p]; simp
+  rw [eq_prod_roots_of_monic_of_splits_id h_mon (IsAlgClosed.splits p)] at nu
   obtain ⟨k, hk, _⟩ := exists_mem_of_not_is_unit_aeval_prod (monic.ne_zero h_mon) nu
   exact ⟨k, hk⟩
 #align spectrum.nonempty_of_is_alg_closed_of_finite_dimensional spectrum.nonempty_of_isAlgClosed_of_finiteDimensional

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -63,7 +63,7 @@ theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A} (hp
   by
   rw [← Multiset.prod_toList, AlgHom.map_list_prod] at h 
   replace h := mt List.prod_isUnit h
-  simp only [not_forall, exists_prop, aeval_C, Multiset.mem_toList, List.mem_map, aeval_X,
+  simp only [Classical.not_forall, exists_prop, aeval_C, Multiset.mem_toList, List.mem_map, aeval_X,
     exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h 
   rcases h with ⟨r, r_mem, r_nu⟩
   exact ⟨r, by rwa [mem_iff, ← IsUnit.sub_iff], by rwa [← is_root.def, ← mem_roots hp]⟩

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathbin.Algebra.Algebra.Spectrum
-import Mathbin.FieldTheory.IsAlgClosed.Basic
+import Algebra.Algebra.Spectrum
+import FieldTheory.IsAlgClosed.Basic
 
 #align_import field_theory.is_alg_closed.spectrum from "leanprover-community/mathlib"@"660b3a2db3522fa0db036e569dc995a615c4c848"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module field_theory.is_alg_closed.spectrum
-! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Spectrum
 import Mathbin.FieldTheory.IsAlgClosed.Basic
 
+#align_import field_theory.is_alg_closed.spectrum from "leanprover-community/mathlib"@"660b3a2db3522fa0db036e569dc995a615c4c848"
+
 /-!
 # Spectrum mapping theorem
 

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

@@ -56,10 +56,8 @@ variable {R : Type u} {A : Type v}
 
 variable [CommRing R] [Ring A] [Algebra R A]
 
--- mathport name: exprσ
 local notation "σ" => spectrum R
 
--- mathport name: «expr↑ₐ»
 local notation "↑ₐ" => algebraMap R A
 
 theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A} (hp : p ≠ 0)
@@ -82,14 +80,13 @@ variable {𝕜 : Type u} {A : Type v}
 
 variable [Field 𝕜] [Ring A] [Algebra 𝕜 A]
 
--- mathport name: exprσ
 local notation "σ" => spectrum 𝕜
 
--- mathport name: «expr↑ₐ»
 local notation "↑ₐ" => algebraMap 𝕜 A
 
 open Polynomial
 
+#print spectrum.subset_polynomial_aeval /-
 /-- Half of the spectral mapping theorem for polynomials. We prove it separately
 because it holds over any field, whereas `spectrum.map_polynomial_aeval_of_degree_pos` and
 `spectrum.map_polynomial_aeval_of_nonempty` need the field to be algebraically closed. -/
@@ -106,7 +103,9 @@ theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (fun k => eval k p) '' 
   apply mt fun h => (hcomm.is_unit_mul_iff.mp h).1
   simpa only [aeval_X, aeval_C, AlgHom.map_sub] using hk
 #align spectrum.subset_polynomial_aeval spectrum.subset_polynomial_aeval
+-/
 
+#print spectrum.map_polynomial_aeval_of_degree_pos /-
 /-- The *spectral mapping theorem* for polynomials.  Note: the assumption `degree p > 0`
 is necessary in case `σ a = ∅`, for then the left-hand side is `∅` and the right-hand side,
 assuming `[nontrivial A]`, is `{k}` where `p = polynomial.C k`. -/
@@ -132,7 +131,9 @@ theorem map_polynomial_aeval_of_degree_pos [IsAlgClosed 𝕜] (a : A) (p : 𝕜[
   rcases hk with ⟨r, r_mem, r_ev⟩
   exact ⟨r, r_mem, symm (by simpa [eval_sub, eval_C, sub_eq_zero] using r_ev)⟩
 #align spectrum.map_polynomial_aeval_of_degree_pos spectrum.map_polynomial_aeval_of_degree_pos
+-/
 
+#print spectrum.map_polynomial_aeval_of_nonempty /-
 /-- In this version of the spectral mapping theorem, we assume the spectrum
 is nonempty instead of assuming the degree of the polynomial is positive. -/
 theorem map_polynomial_aeval_of_nonempty [IsAlgClosed 𝕜] (a : A) (p : 𝕜[X])
@@ -143,12 +144,16 @@ theorem map_polynomial_aeval_of_nonempty [IsAlgClosed 𝕜] (a : A) (p : 𝕜[X]
   · rw [eq_C_of_degree_le_zero h]
     simp only [Set.image_congr, eval_C, aeval_C, scalar_eq, Set.Nonempty.image_const hnon]
 #align spectrum.map_polynomial_aeval_of_nonempty spectrum.map_polynomial_aeval_of_nonempty
+-/
 
+#print spectrum.pow_image_subset /-
 /-- A specialization of `spectrum.subset_polynomial_aeval` to monic monomials for convenience. -/
 theorem pow_image_subset (a : A) (n : ℕ) : (fun x => x ^ n) '' σ a ⊆ σ (a ^ n) := by
   simpa only [eval_pow, eval_X, aeval_X_pow] using subset_polynomial_aeval a (X ^ n : 𝕜[X])
 #align spectrum.pow_image_subset spectrum.pow_image_subset
+-/
 
+#print spectrum.map_pow_of_pos /-
 /-- A specialization of `spectrum.map_polynomial_aeval_of_nonempty` to monic monomials for
 convenience. -/
 theorem map_pow_of_pos [IsAlgClosed 𝕜] (a : A) {n : ℕ} (hn : 0 < n) :
@@ -156,13 +161,16 @@ theorem map_pow_of_pos [IsAlgClosed 𝕜] (a : A) {n : ℕ} (hn : 0 < n) :
   simpa only [aeval_X_pow, eval_pow, eval_X] using
     map_polynomial_aeval_of_degree_pos a (X ^ n : 𝕜[X]) (by rw_mod_cast [degree_X_pow]; exact hn)
 #align spectrum.map_pow_of_pos spectrum.map_pow_of_pos
+-/
 
+#print spectrum.map_pow_of_nonempty /-
 /-- A specialization of `spectrum.map_polynomial_aeval_of_nonempty` to monic monomials for
 convenience. -/
 theorem map_pow_of_nonempty [IsAlgClosed 𝕜] {a : A} (ha : (σ a).Nonempty) (n : ℕ) :
     σ (a ^ n) = (fun x => x ^ n) '' σ a := by
   simpa only [aeval_X_pow, eval_pow, eval_X] using map_polynomial_aeval_of_nonempty a (X ^ n) ha
 #align spectrum.map_pow_of_nonempty spectrum.map_pow_of_nonempty
+-/
 
 variable (𝕜)
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module field_theory.is_alg_closed.spectrum
-! leanprover-community/mathlib commit 58a272265b5e05f258161260dd2c5d247213cbd3
+! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
 ! 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.IsAlgClosed.Basic
 /-!
 # Spectrum mapping theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file develops proves the spectral mapping theorem for polynomials over algebraically closed
 fields. In particular, if `a` is an element of an `𝕜`-algebra `A` where `𝕜` is a field, and
 `p : 𝕜[X]` is a polynomial, then the spectrum of `polynomial.aeval a p` contains the image of the

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

@@ -69,7 +69,7 @@ theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A} (hp
     exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h 
   rcases h with ⟨r, r_mem, r_nu⟩
   exact ⟨r, by rwa [mem_iff, ← IsUnit.sub_iff], by rwa [← is_root.def, ← mem_roots hp]⟩
-#align spectrum.exists_mem_of_not_is_unit_aeval_prod spectrum.exists_mem_of_not_isUnit_aeval_prod
+#align spectrum.exists_mem_of_not_is_unit_aeval_prod spectrum.exists_mem_of_not_isUnit_aeval_prodₓ
 
 end ScalarRing
 
@@ -163,6 +163,7 @@ theorem map_pow_of_nonempty [IsAlgClosed 𝕜] {a : A} (ha : (σ a).Nonempty) (n
 
 variable (𝕜)
 
+#print spectrum.nonempty_of_isAlgClosed_of_finiteDimensional /-
 -- We will use this both to show eigenvalues exist, and to prove Schur's lemma.
 /-- Every element `a` in a nontrivial finite-dimensional algebra `A`
 over an algebraically closed field `𝕜` has non-empty spectrum. -/
@@ -175,6 +176,7 @@ theorem nonempty_of_isAlgClosed_of_finiteDimensional [IsAlgClosed 𝕜] [Nontriv
   obtain ⟨k, hk, _⟩ := exists_mem_of_not_is_unit_aeval_prod (monic.ne_zero h_mon) nu
   exact ⟨k, hk⟩
 #align spectrum.nonempty_of_is_alg_closed_of_finite_dimensional spectrum.nonempty_of_isAlgClosed_of_finiteDimensional
+-/
 
 end ScalarField
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

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

@@ -81,7 +81,7 @@ because it holds over any field, whereas `spectrum.map_polynomial_aeval_of_degre
 theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (eval · p) '' σ a ⊆ σ (aeval a p) := by
   rintro _ ⟨k, hk, rfl⟩
   let q := C (eval k p) - p
-  have hroot : IsRoot q k := by simp only [q, eval_C, eval_sub, sub_self, IsRoot.definition]
+  have hroot : IsRoot q k := by simp only [q, eval_C, eval_sub, sub_self, IsRoot.def]
   rw [← mul_div_eq_iff_isRoot, ← neg_mul_neg, neg_sub] at hroot
   have aeval_q_eq : ↑ₐ (eval k p) - aeval a p = aeval a q := by
     simp only [q, aeval_C, AlgHom.map_sub, sub_left_inj]

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -81,7 +81,7 @@ because it holds over any field, whereas `spectrum.map_polynomial_aeval_of_degre
 theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (eval · p) '' σ a ⊆ σ (aeval a p) := by
   rintro _ ⟨k, hk, rfl⟩
   let q := C (eval k p) - p
-  have hroot : IsRoot q k := by simp only [q, eval_C, eval_sub, sub_self, IsRoot.def]
+  have hroot : IsRoot q k := by simp only [q, eval_C, eval_sub, sub_self, IsRoot.definition]
   rw [← mul_div_eq_iff_isRoot, ← neg_mul_neg, neg_sub] at hroot
   have aeval_q_eq : ↑ₐ (eval k p) - aeval a p = aeval a q := by
     simp only [q, aeval_C, AlgHom.map_sub, sub_left_inj]

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)

@@ -46,7 +46,6 @@ universe u v
 section ScalarRing
 
 variable {R : Type u} {A : Type v}
-
 variable [CommRing R] [Ring A] [Algebra R A]
 
 local notation "σ" => spectrum R
@@ -69,7 +68,6 @@ end ScalarRing
 section ScalarField
 
 variable {𝕜 : Type u} {A : Type v}
-
 variable [Field 𝕜] [Ring A] [Algebra 𝕜 A]
 
 local notation "σ" => spectrum 𝕜

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -14,9 +14,9 @@ import Mathlib.FieldTheory.IsAlgClosed.Basic
 This file develops proves the spectral mapping theorem for polynomials over algebraically closed
 fields. In particular, if `a` is an element of a `𝕜`-algebra `A` where `𝕜` is a field, and
 `p : 𝕜[X]` is a polynomial, then the spectrum of `Polynomial.aeval a p` contains the image of the
-spectrum of `a` under `(λ k, Polynomial.eval k p)`. When `𝕜` is algebraically closed, these are in
-fact equal (assuming either that the spectrum of `a` is nonempty or the polynomial has positive
-degree), which is the **spectral mapping theorem**.
+spectrum of `a` under `(fun k ↦ Polynomial.eval k p)`. When `𝕜` is algebraically closed,
+these are in fact equal (assuming either that the spectrum of `a` is nonempty or the polynomial
+has positive degree), which is the **spectral mapping theorem**.
 
 In addition, this file contains the fact that every element of a finite dimensional nontrivial
 algebra over an algebraically closed field has nonempty spectrum. In particular, this is used in

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -52,7 +52,7 @@ variable [CommRing R] [Ring A] [Algebra R A]
 local notation "σ" => spectrum R
 local notation "↑ₐ" => algebraMap R A
 
--- porting note: removed an unneeded assumption `p ≠ 0`
+-- Porting note: removed an unneeded assumption `p ≠ 0`
 theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A}
     (h : ¬IsUnit (aeval a (Multiset.map (fun x : R => X - C x) p.roots).prod)) :
     ∃ k : R, k ∈ σ a ∧ eval k p = 0 := by

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

@@ -83,10 +83,10 @@ because it holds over any field, whereas `spectrum.map_polynomial_aeval_of_degre
 theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (eval · p) '' σ a ⊆ σ (aeval a p) := by
   rintro _ ⟨k, hk, rfl⟩
   let q := C (eval k p) - p
-  have hroot : IsRoot q k := by simp only [eval_C, eval_sub, sub_self, IsRoot.def]
+  have hroot : IsRoot q k := by simp only [q, eval_C, eval_sub, sub_self, IsRoot.def]
   rw [← mul_div_eq_iff_isRoot, ← neg_mul_neg, neg_sub] at hroot
   have aeval_q_eq : ↑ₐ (eval k p) - aeval a p = aeval a q := by
-    simp only [aeval_C, AlgHom.map_sub, sub_left_inj]
+    simp only [q, aeval_C, AlgHom.map_sub, sub_left_inj]
   rw [mem_iff, aeval_q_eq, ← hroot, aeval_mul]
   have hcomm := (Commute.all (C k - X) (-(q / (X - C k)))).map (aeval a : 𝕜[X] →ₐ[𝕜] A)
   apply mt fun h => (hcomm.isUnit_mul_iff.mp h).1

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -35,8 +35,6 @@ eigenvalue.
 * `σ a` : `spectrum R a` of `a : A`
 -/
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 namespace spectrum
 
 open Set Polynomial

@@ -35,7 +35,7 @@ eigenvalue.
 * `σ a` : `spectrum R a` of `a : A`
 -/
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 namespace spectrum
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module field_theory.is_alg_closed.spectrum
-! leanprover-community/mathlib commit 58a272265b5e05f258161260dd2c5d247213cbd3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Spectrum
 import Mathlib.FieldTheory.IsAlgClosed.Basic
 
+#align_import field_theory.is_alg_closed.spectrum from "leanprover-community/mathlib"@"58a272265b5e05f258161260dd2c5d247213cbd3"
+
 /-!
 # Spectrum mapping theorem
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -160,7 +160,7 @@ over an algebraically closed field `𝕜` has non-empty spectrum. -/
 theorem nonempty_of_isAlgClosed_of_finiteDimensional [IsAlgClosed 𝕜] [Nontrivial A]
     [I : FiniteDimensional 𝕜 A] (a : A) : (σ a).Nonempty := by
   obtain ⟨p, ⟨h_mon, h_eval_p⟩⟩ := isIntegral_of_noetherian (IsNoetherian.iff_fg.2 I) a
-  have nu : ¬IsUnit (aeval a p) := by rw [← aeval_def] at h_eval_p ; rw [h_eval_p]; simp
+  have nu : ¬IsUnit (aeval a p) := by rw [← aeval_def] at h_eval_p; rw [h_eval_p]; simp
   rw [eq_prod_roots_of_monic_of_splits_id h_mon (IsAlgClosed.splits p)] at nu
   obtain ⟨k, hk, _⟩ := exists_mem_of_not_isUnit_aeval_prod nu
   exact ⟨k, hk⟩

@@ -23,7 +23,7 @@ degree), which is the **spectral mapping theorem**.
 
 In addition, this file contains the fact that every element of a finite dimensional nontrivial
 algebra over an algebraically closed field has nonempty spectrum. In particular, this is used in
-`module.End.exists_eigenvalue` to show that every linear map from a vector space to itself has an
+`Module.End.exists_eigenvalue` to show that every linear map from a vector space to itself has an
 eigenvalue.
 
 ## Main statements
@@ -61,10 +61,10 @@ local notation "↑ₐ" => algebraMap R A
 theorem exists_mem_of_not_isUnit_aeval_prod [IsDomain R] {p : R[X]} {a : A}
     (h : ¬IsUnit (aeval a (Multiset.map (fun x : R => X - C x) p.roots).prod)) :
     ∃ k : R, k ∈ σ a ∧ eval k p = 0 := by
-  rw [← Multiset.prod_toList, AlgHom.map_list_prod] at h 
+  rw [← Multiset.prod_toList, AlgHom.map_list_prod] at h
   replace h := mt List.prod_isUnit h
   simp only [not_forall, exists_prop, aeval_C, Multiset.mem_toList, List.mem_map, aeval_X,
-    exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h 
+    exists_exists_and_eq_and, Multiset.mem_map, AlgHom.map_sub] at h
   rcases h with ⟨r, r_mem, r_nu⟩
   exact ⟨r, by rwa [mem_iff, ← IsUnit.sub_iff], (mem_roots'.1 r_mem).2⟩
 #align spectrum.exists_mem_of_not_is_unit_aeval_prod spectrum.exists_mem_of_not_isUnit_aeval_prodₓ
@@ -89,7 +89,7 @@ theorem subset_polynomial_aeval (a : A) (p : 𝕜[X]) : (eval · p) '' σ a ⊆
   rintro _ ⟨k, hk, rfl⟩
   let q := C (eval k p) - p
   have hroot : IsRoot q k := by simp only [eval_C, eval_sub, sub_self, IsRoot.def]
-  rw [← mul_div_eq_iff_isRoot, ← neg_mul_neg, neg_sub] at hroot 
+  rw [← mul_div_eq_iff_isRoot, ← neg_mul_neg, neg_sub] at hroot
   have aeval_q_eq : ↑ₐ (eval k p) - aeval a p = aeval a q := by
     simp only [aeval_C, AlgHom.map_sub, sub_left_inj]
   rw [mem_iff, aeval_q_eq, ← hroot, aeval_mul]
@@ -161,7 +161,7 @@ theorem nonempty_of_isAlgClosed_of_finiteDimensional [IsAlgClosed 𝕜] [Nontriv
     [I : FiniteDimensional 𝕜 A] (a : A) : (σ a).Nonempty := by
   obtain ⟨p, ⟨h_mon, h_eval_p⟩⟩ := isIntegral_of_noetherian (IsNoetherian.iff_fg.2 I) a
   have nu : ¬IsUnit (aeval a p) := by rw [← aeval_def] at h_eval_p ; rw [h_eval_p]; simp
-  rw [eq_prod_roots_of_monic_of_splits_id h_mon (IsAlgClosed.splits p)] at nu 
+  rw [eq_prod_roots_of_monic_of_splits_id h_mon (IsAlgClosed.splits p)] at nu
   obtain ⟨k, hk, _⟩ := exists_mem_of_not_isUnit_aeval_prod nu
   exact ⟨k, hk⟩
 #align spectrum.nonempty_of_is_alg_closed_of_finite_dimensional spectrum.nonempty_of_isAlgClosed_of_finiteDimensional

Part 2 of #5001

@@ -15,7 +15,7 @@ import Mathlib.FieldTheory.IsAlgClosed.Basic
 # Spectrum mapping theorem
 
 This file develops proves the spectral mapping theorem for polynomials over algebraically closed
-fields. In particular, if `a` is an element of an `𝕜`-algebra `A` where `𝕜` is a field, and
+fields. In particular, if `a` is an element of a `𝕜`-algebra `A` where `𝕜` is a field, and
 `p : 𝕜[X]` is a polynomial, then the spectrum of `Polynomial.aeval a p` contains the image of the
 spectrum of `a` under `(λ k, Polynomial.eval k p)`. When `𝕜` is algebraically closed, these are in
 fact equal (assuming either that the spectrum of `a` is nonempty or the polynomial has positive