field_theory.is_alg_closed.classification

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

0723536a

(last sync)

chore(data/zmod/algebra): make zmod.algebra a def (#19197)

zmod.algebra creates a diamond about the zmod p-algebra structure on zmod p:

import algebra.algebra.basic
import data.zmod.algebra

example (p : ℕ) : algebra.id (zmod p) =
  (zmod.algebra (zmod p) p) := rfl --fails

This is also causing troubles with the port. We turn zmod.algebra into a def.

Diff

@@ -158,10 +158,9 @@ variables {K L : Type} [field K] [field L] [is_alg_closed K] [is_alg_closed L]
 
 /-- Two uncountable algebraically closed fields of characteristic zero are isomorphic
 if they have the same cardinality. -/
-@[nolint def_lemma] lemma ring_equiv_of_cardinal_eq_of_char_zero [char_zero K] [char_zero L]
-  (hK : ℵ₀ < #K) (hKL : #K = #L) : K ≃+* L :=
+lemma ring_equiv_of_cardinal_eq_of_char_zero [char_zero K] [char_zero L]
+  (hK : ℵ₀ < #K) (hKL : #K = #L) : nonempty (K ≃+* L) :=
 begin
-  apply classical.choice,
   cases exists_is_transcendence_basis ℤ
     (show function.injective (algebra_map ℤ K),
       from int.cast_injective) with s hs,
@@ -177,9 +176,10 @@ begin
 end
 
 private lemma ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [fact p.prime]
-  [char_p K p] [char_p L p] (hK : ℵ₀ < #K) (hKL : #K = #L) : K ≃+* L :=
+  [char_p K p] [char_p L p] (hK : ℵ₀ < #K) (hKL : #K = #L) : nonempty (K ≃+* L) :=
 begin
-  apply classical.choice,
+  letI : algebra (zmod p) K := zmod.algebra _ _,
+  letI : algebra (zmod p) L := zmod.algebra _ _,
   cases exists_is_transcendence_basis (zmod p)
     (show function.injective (algebra_map (zmod p) K),
       from ring_hom.injective _) with s hs,
@@ -198,18 +198,19 @@ end
 
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/
-@[nolint def_lemma] lemma ring_equiv_of_cardinal_eq_of_char_eq (p : ℕ) [char_p K p] [char_p L p]
-  (hK : ℵ₀ < #K) (hKL : #K = #L) : K ≃+* L :=
+lemma ring_equiv_of_cardinal_eq_of_char_eq (p : ℕ) [char_p K p] [char_p L p]
+  (hK : ℵ₀ < #K) (hKL : #K = #L) : nonempty (K ≃+* L) :=
 begin
-  apply classical.choice,
   rcases char_p.char_is_prime_or_zero K p with hp | hp,
   { haveI : fact p.prime := ⟨hp⟩,
-    exact ⟨ring_equiv_of_cardinal_eq_of_char_p p hK hKL⟩ },
+    letI : algebra (zmod p) K := zmod.algebra _ _,
+    letI : algebra (zmod p) L := zmod.algebra _ _,
+    exact ring_equiv_of_cardinal_eq_of_char_p p hK hKL },
   { rw [hp] at *,
     resetI,
     letI : char_zero K := char_p.char_p_to_char_zero K,
     letI : char_zero L := char_p.char_p_to_char_zero L,
-    exact ⟨ring_equiv_of_cardinal_eq_of_char_zero hK hKL⟩ }
+    exact ring_equiv_of_cardinal_eq_of_char_zero hK hKL }
 end
 
 end is_alg_closed

70fd9563

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

0723536a

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -5,8 +5,8 @@ Authors: Chris Hughes
 -/
 import RingTheory.AlgebraicIndependent
 import FieldTheory.IsAlgClosed.Basic
-import Data.Polynomial.Cardinal
-import Data.MvPolynomial.Cardinal
+import Algebra.Polynomial.Cardinal
+import Algebra.MvPolynomial.Cardinal
 import Data.ZMod.Algebra
 
 #align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"

0723536a

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -7,7 +7,7 @@ import RingTheory.AlgebraicIndependent
 import FieldTheory.IsAlgClosed.Basic
 import Data.Polynomial.Cardinal
 import Data.MvPolynomial.Cardinal
-import Data.Zmod.Algebra
+import Data.ZMod.Algebra
 
 #align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"

0723536a

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -60,7 +60,7 @@ theorem cardinal_mk_le_sigma_polynomial :
           p.2.2]⟩)
     fun x y => by
     intro h
-    simp only at h 
+    simp only at h
     refine' (Subtype.heq_iff_coe_eq _).1 h.2
     simp only [h.1, iff_self_iff, forall_true_iff]
 #align algebra.is_algebraic.cardinal_mk_le_sigma_polynomial Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial

0723536a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2022 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.RingTheory.AlgebraicIndependent
-import Mathbin.FieldTheory.IsAlgClosed.Basic
-import Mathbin.Data.Polynomial.Cardinal
-import Mathbin.Data.MvPolynomial.Cardinal
-import Mathbin.Data.Zmod.Algebra
+import RingTheory.AlgebraicIndependent
+import FieldTheory.IsAlgClosed.Basic
+import Data.Polynomial.Cardinal
+import Data.MvPolynomial.Cardinal
+import Data.Zmod.Algebra
 
 #align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"

0723536a

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -34,7 +34,7 @@ open scoped Cardinal Polynomial
 
 open Cardinal
 
-section AlgebraicClosure
+section AlgebraicClosureAux
 
 namespace Algebra.IsAlgebraic
 
@@ -87,7 +87,7 @@ theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
 
 end Algebra.IsAlgebraic
 
-end AlgebraicClosure
+end AlgebraicClosureAux
 
 namespace IsAlgClosed

0723536a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.AlgebraicIndependent
 import Mathbin.FieldTheory.IsAlgClosed.Basic
@@ -14,6 +9,8 @@ import Mathbin.Data.Polynomial.Cardinal
 import Mathbin.Data.MvPolynomial.Cardinal
 import Mathbin.Data.Zmod.Algebra
 
+#align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
+
 /-!
 # Classification of Algebraically closed fields

0723536a

bump to nightly-2023-06-20-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

1fb3229c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
-! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
+! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -196,10 +196,9 @@ variable {K L : Type} [Field K] [Field L] [IsAlgClosed K] [IsAlgClosed L]
 #print IsAlgClosed.ringEquivOfCardinalEqOfCharZero /-
 /-- Two uncountable algebraically closed fields of characteristic zero are isomorphic
 if they have the same cardinality. -/
-@[nolint def_lemma]
 theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : K ≃+* L := by
-  apply Classical.choice
+    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) :=
+  by
   cases'
     exists_isTranscendenceBasis ℤ
       (show Function.Injective (algebraMap ℤ K) from Int.cast_injective) with
@@ -219,9 +218,10 @@ theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ <
 -/
 
 private theorem ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [Fact p.Prime] [CharP K p] [CharP L p]
-    (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : K ≃+* L :=
+    (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) :=
   by
-  apply Classical.choice
+  letI : Algebra (ZMod p) K := ZMod.algebra _ _
+  letI : Algebra (ZMod p) L := ZMod.algebra _ _
   cases'
     exists_isTranscendenceBasis (ZMod p)
       (show Function.Injective (algebraMap (ZMod p) K) from RingHom.injective _) with
@@ -246,18 +246,19 @@ private theorem ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [Fact p.Prime] [Ch
 #print IsAlgClosed.ringEquivOfCardinalEqOfCharEq /-
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/
-@[nolint def_lemma]
 theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : K ≃+* L := by
-  apply Classical.choice
+    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) :=
+  by
   rcases CharP.char_is_prime_or_zero K p with (hp | hp)
   · haveI : Fact p.prime := ⟨hp⟩
-    exact ⟨ring_equiv_of_cardinal_eq_of_char_p p hK hKL⟩
+    letI : Algebra (ZMod p) K := ZMod.algebra _ _
+    letI : Algebra (ZMod p) L := ZMod.algebra _ _
+    exact ring_equiv_of_cardinal_eq_of_char_p p hK hKL
   · rw [hp] at *
     skip
     letI : CharZero K := CharP.charP_to_charZero K
     letI : CharZero L := CharP.charP_to_charZero L
-    exact ⟨ring_equiv_of_cardinal_eq_of_char_zero hK hKL⟩
+    exact ring_equiv_of_cardinal_eq_of_char_zero hK hKL
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_eq IsAlgClosed.ringEquivOfCardinalEqOfCharEq
 -/

660b3a2d

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -45,6 +45,7 @@ variable (R L : Type u) [CommRing R] [CommRing L] [IsDomain L] [Algebra R L]
 
 variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
+#print Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial /-
 theorem cardinal_mk_le_sigma_polynomial :
     (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
   @mk_le_of_injective L (Σ p : R[X], {x : L | x ∈ (p.map (algebraMap R L)).roots})
@@ -66,7 +67,9 @@ theorem cardinal_mk_le_sigma_polynomial :
     refine' (Subtype.heq_iff_coe_eq _).1 h.2
     simp only [h.1, iff_self_iff, forall_true_iff]
 #align algebra.is_algebraic.cardinal_mk_le_sigma_polynomial Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial
+-/
 
+#print Algebra.IsAlgebraic.cardinal_mk_le_max /-
 /-- The cardinality of an algebraic extension is at most the maximum of the cardinality
 of the base ring or `ℵ₀` -/
 theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
@@ -83,6 +86,7 @@ theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
       (max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl)
     _ = max (#R) ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
 #align algebra.is_algebraic.cardinal_mk_le_max Algebra.IsAlgebraic.cardinal_mk_le_max
+-/
 
 end Algebra.IsAlgebraic
 
@@ -106,15 +110,18 @@ variable {κ : Type _} (w : κ → L)
 
 variable (hv : AlgebraicIndependent R v)
 
+#print IsAlgClosed.isAlgClosure_of_transcendence_basis /-
 theorem isAlgClosure_of_transcendence_basis [IsAlgClosed K] (hv : IsTranscendenceBasis R v) :
     IsAlgClosure (Algebra.adjoin R (Set.range v)) K :=
   letI := RingHom.domain_nontrivial (algebraMap R K)
   { alg_closed := by infer_instance
     algebraic := hv.is_algebraic }
 #align is_alg_closed.is_alg_closure_of_transcendence_basis IsAlgClosed.isAlgClosure_of_transcendence_basis
+-/
 
 variable (hw : AlgebraicIndependent R w)
 
+#print IsAlgClosed.equivOfTranscendenceBasis /-
 /-- setting `R` to be `zmod (ring_char R)` this result shows that if two algebraically
 closed fields have equipotent transcendence bases and the same characteristic then they are
 isomorphic. -/
@@ -133,6 +140,7 @@ def equivOfTranscendenceBasis [IsAlgClosed K] [IsAlgClosed L] (e : ι ≃ κ)
     exact hw.1.aevalEquiv.toRingEquiv
   exact IsAlgClosure.equivOfEquiv K L e
 #align is_alg_closed.equiv_of_transcendence_basis IsAlgClosed.equivOfTranscendenceBasis
+-/
 
 end Classification
 
@@ -146,6 +154,7 @@ variable {ι : Type u} (v : ι → K)
 
 variable (hv : IsTranscendenceBasis R v)
 
+#print IsAlgClosed.cardinal_le_max_transcendence_basis /-
 theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
     (#K) ≤ max (max (#R) (#ι)) ℵ₀ :=
   calc
@@ -156,6 +165,7 @@ theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
     _ ≤ max (max (max (#R) (#ι)) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
     _ = _ := by simp [max_assoc]
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis
+-/
 
 #print IsAlgClosed.cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt /-
 /-- If `K` is an uncountable algebraically closed field, then its
@@ -183,6 +193,7 @@ end Cardinal
 
 variable {K L : Type} [Field K] [Field L] [IsAlgClosed K] [IsAlgClosed L]
 
+#print IsAlgClosed.ringEquivOfCardinalEqOfCharZero /-
 /-- Two uncountable algebraically closed fields of characteristic zero are isomorphic
 if they have the same cardinality. -/
 @[nolint def_lemma]
@@ -205,6 +216,7 @@ theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ <
   cases' Cardinal.eq.1 this with e
   exact ⟨equiv_of_transcendence_basis _ _ e hs ht⟩
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_zero IsAlgClosed.ringEquivOfCardinalEqOfCharZero
+-/
 
 private theorem ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [Fact p.Prime] [CharP K p] [CharP L p]
     (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : K ≃+* L :=
@@ -231,6 +243,7 @@ private theorem ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [Fact p.Prime] [Ch
   cases' Cardinal.eq.1 this with e
   exact ⟨equiv_of_transcendence_basis _ _ e hs ht⟩
 
+#print IsAlgClosed.ringEquivOfCardinalEqOfCharEq /-
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/
 @[nolint def_lemma]
@@ -246,6 +259,7 @@ theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : 
     letI : CharZero L := CharP.charP_to_charZero L
     exact ⟨ring_equiv_of_cardinal_eq_of_char_zero hK hKL⟩
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_eq IsAlgClosed.ringEquivOfCardinalEqOfCharEq
+-/
 
 end IsAlgClosed

660b3a2d

bump to nightly-2023-06-12-03

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

879d466d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Data.Zmod.Algebra
 /-!
 # Classification of Algebraically closed fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains results related to classifying algebraically closed fields.
 
 ## Main statements

70fd9563

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -154,6 +154,7 @@ theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
     _ = _ := by simp [max_assoc]
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis
 
+#print IsAlgClosed.cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt /-
 /-- If `K` is an uncountable algebraically closed field, then its
 cardinality is the same as that of a transcendence basis. -/
 theorem cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt [Nontrivial R]
@@ -173,6 +174,7 @@ theorem cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt [Nontrivial R]
         · exact le_max_of_le_right this)
     (mk_le_of_injective (show Function.Injective v from hv.1.Injective))
 #align is_alg_closed.cardinal_eq_cardinal_transcendence_basis_of_aleph_0_lt IsAlgClosed.cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt
+-/
 
 end Cardinal

70fd9563

bump to nightly-2023-06-10-01

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

8c45e6a5

Diff

@@ -103,12 +103,12 @@ variable {κ : Type _} (w : κ → L)
 
 variable (hv : AlgebraicIndependent R v)
 
-theorem isAlgClosureOfTranscendenceBasis [IsAlgClosed K] (hv : IsTranscendenceBasis R v) :
+theorem isAlgClosure_of_transcendence_basis [IsAlgClosed K] (hv : IsTranscendenceBasis R v) :
     IsAlgClosure (Algebra.adjoin R (Set.range v)) K :=
   letI := RingHom.domain_nontrivial (algebraMap R K)
   { alg_closed := by infer_instance
     algebraic := hv.is_algebraic }
-#align is_alg_closed.is_alg_closure_of_transcendence_basis IsAlgClosed.isAlgClosureOfTranscendenceBasis
+#align is_alg_closed.is_alg_closure_of_transcendence_basis IsAlgClosed.isAlgClosure_of_transcendence_basis
 
 variable (hw : AlgebraicIndependent R w)

70fd9563

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -79,7 +79,6 @@ theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
     _ ≤ max (max (max (#R) ℵ₀) ℵ₀) ℵ₀ :=
       (max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl)
     _ = max (#R) ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
-    
 #align algebra.is_algebraic.cardinal_mk_le_max Algebra.IsAlgebraic.cardinal_mk_le_max
 
 end Algebra.IsAlgebraic
@@ -153,7 +152,6 @@ theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
     _ = max (#MvPolynomial ι R) ℵ₀ := by rw [Cardinal.eq.2 ⟨hv.1.aevalEquiv.toEquiv⟩]
     _ ≤ max (max (max (#R) (#ι)) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
     _ = _ := by simp [max_assoc]
-    
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis
 
 /-- If `K` is an uncountable algebraically closed field, then its
@@ -166,15 +164,13 @@ theorem cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt [Nontrivial R]
         calc
           (#K) ≤ max (max (#R) (#ι)) ℵ₀ := cardinal_le_max_transcendence_basis v hv
           _ ≤ _ := max_le (max_le hR (le_of_lt h)) le_rfl
-          
   le_antisymm
     (calc
       (#K) ≤ max (max (#R) (#ι)) ℵ₀ := cardinal_le_max_transcendence_basis v hv
       _ = (#ι) := by
         rw [max_eq_left, max_eq_right]
         · exact le_trans hR this
-        · exact le_max_of_le_right this
-      )
+        · exact le_max_of_le_right this)
     (mk_le_of_injective (show Function.Injective v from hv.1.Injective))
 #align is_alg_closed.cardinal_eq_cardinal_transcendence_basis_of_aleph_0_lt IsAlgClosed.cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt

70fd9563

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -44,7 +44,7 @@ variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
 theorem cardinal_mk_le_sigma_polynomial :
     (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
-  @mk_le_of_injective L (Σ p : R[X], { x : L | x ∈ (p.map (algebraMap R L)).roots })
+  @mk_le_of_injective L (Σ p : R[X], {x : L | x ∈ (p.map (algebraMap R L)).roots})
     (fun x : L =>
       let p := Classical.indefiniteDescription _ (halg x)
       ⟨p.1, x, by
@@ -70,7 +70,7 @@ theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
   calc
     (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
       cardinal_mk_le_sigma_polynomial R L halg
-    _ = Cardinal.sum fun p : R[X] => #{ x : L | x ∈ (p.map (algebraMap R L)).roots } := by
+    _ = Cardinal.sum fun p : R[X] => #{x : L | x ∈ (p.map (algebraMap R L)).roots} := by
       rw [← mk_sigma] <;> rfl
     _ ≤ Cardinal.sum.{u, u} fun p : R[X] => ℵ₀ :=
       (sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le)

70fd9563

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -43,8 +43,8 @@ variable (R L : Type u) [CommRing R] [CommRing L] [IsDomain L] [Algebra R L]
 variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
 theorem cardinal_mk_le_sigma_polynomial :
-    (#L) ≤ (#Σp : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
-  @mk_le_of_injective L (Σp : R[X], { x : L | x ∈ (p.map (algebraMap R L)).roots })
+    (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
+  @mk_le_of_injective L (Σ p : R[X], { x : L | x ∈ (p.map (algebraMap R L)).roots })
     (fun x : L =>
       let p := Classical.indefiniteDescription _ (halg x)
       ⟨p.1, x, by
@@ -59,7 +59,7 @@ theorem cardinal_mk_le_sigma_polynomial :
           p.2.2]⟩)
     fun x y => by
     intro h
-    simp only at h
+    simp only at h 
     refine' (Subtype.heq_iff_coe_eq _).1 h.2
     simp only [h.1, iff_self_iff, forall_true_iff]
 #align algebra.is_algebraic.cardinal_mk_le_sigma_polynomial Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial
@@ -68,7 +68,7 @@ theorem cardinal_mk_le_sigma_polynomial :
 of the base ring or `ℵ₀` -/
 theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
   calc
-    (#L) ≤ (#Σp : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
+    (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
       cardinal_mk_le_sigma_polynomial R L halg
     _ = Cardinal.sum fun p : R[X] => #{ x : L | x ∈ (p.map (algebraMap R L)).roots } := by
       rw [← mk_sigma] <;> rfl

70fd9563

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -30,7 +30,7 @@ This file contains results related to classifying algebraically closed fields.
 
 universe u
 
-open Cardinal Polynomial
+open scoped Cardinal Polynomial
 
 open Cardinal

70fd9563

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -126,10 +126,8 @@ def equivOfTranscendenceBasis [IsAlgClosed K] [IsAlgClosed L] (e : ι ≃ κ)
     refine'
       (AlgEquiv.ofAlgHom (MvPolynomial.rename e) (MvPolynomial.rename e.symm) _ _).toRingEquiv.trans
         _
-    · ext
-      simp
-    · ext
-      simp
+    · ext; simp
+    · ext; simp
     exact hw.1.aevalEquiv.toRingEquiv
   exact IsAlgClosure.equivOfEquiv K L e
 #align is_alg_closed.equiv_of_transcendence_basis IsAlgClosed.equivOfTranscendenceBasis

70fd9563

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -231,7 +231,6 @@ private theorem ring_equiv_of_cardinal_eq_of_char_p (p : ℕ) [Fact p.Prime] [Ch
     rwa [← hKL]
   cases' Cardinal.eq.1 this with e
   exact ⟨equiv_of_transcendence_basis _ _ e hs ht⟩
-#align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_p is_alg_closed.ring_equiv_of_cardinal_eq_of_char_p
 
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/

70fd9563

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -73,11 +73,11 @@ theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
     _ = Cardinal.sum fun p : R[X] => #{ x : L | x ∈ (p.map (algebraMap R L)).roots } := by
       rw [← mk_sigma] <;> rfl
     _ ≤ Cardinal.sum.{u, u} fun p : R[X] => ℵ₀ :=
-      sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le
-    _ = (#R[X]) * ℵ₀ := sum_const' _ _
-    _ ≤ max (max (#R[X]) ℵ₀) ℵ₀ := mul_le_max _ _
+      (sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le)
+    _ = (#R[X]) * ℵ₀ := (sum_const' _ _)
+    _ ≤ max (max (#R[X]) ℵ₀) ℵ₀ := (mul_le_max _ _)
     _ ≤ max (max (max (#R) ℵ₀) ℵ₀) ℵ₀ :=
-      max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl
+      (max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl)
     _ = max (#R) ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
     
 #align algebra.is_algebraic.cardinal_mk_le_max Algebra.IsAlgebraic.cardinal_mk_le_max
@@ -153,7 +153,7 @@ theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
       letI := is_alg_closure_of_transcendence_basis v hv
       Algebra.IsAlgebraic.cardinal_mk_le_max _ _ IsAlgClosure.algebraic
     _ = max (#MvPolynomial ι R) ℵ₀ := by rw [Cardinal.eq.2 ⟨hv.1.aevalEquiv.toEquiv⟩]
-    _ ≤ max (max (max (#R) (#ι)) ℵ₀) ℵ₀ := max_le_max MvPolynomial.cardinal_mk_le_max le_rfl
+    _ ≤ max (max (max (#R) (#ι)) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
     _ = _ := by simp [max_assoc]
     
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

0723536a

chore: superfluous parentheses part 2 (#12131)

Co-authored-by: Moritz Firsching <firsching@google.com>

d48d30ac

Diff

@@ -69,8 +69,8 @@ theorem cardinal_mk_le_max : #L ≤ max #R ℵ₀ :=
       rw [← mk_sigma]; rfl
     _ ≤ Cardinal.sum.{u, u} fun _ : R[X] => ℵ₀ :=
       (sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le)
-    _ = #(R[X]) * ℵ₀ := (sum_const' _ _)
-    _ ≤ max (max #(R[X]) ℵ₀) ℵ₀ := (mul_le_max _ _)
+    _ = #(R[X]) * ℵ₀ := sum_const' _ _
+    _ ≤ max (max #(R[X]) ℵ₀) ℵ₀ := mul_le_max _ _
     _ ≤ max (max (max #R ℵ₀) ℵ₀) ℵ₀ :=
       (max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl)
     _ = max #R ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
@@ -137,7 +137,7 @@ theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
       letI := isAlgClosure_of_transcendence_basis v hv
       Algebra.IsAlgebraic.cardinal_mk_le_max _ _ IsAlgClosure.algebraic
     _ = max #(MvPolynomial ι R) ℵ₀ := by rw [Cardinal.eq.2 ⟨hv.1.aevalEquiv.toEquiv⟩]
-    _ ≤ max (max (max #R #ι) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
+    _ ≤ max (max (max #R #ι) ℵ₀) ℵ₀ := max_le_max MvPolynomial.cardinal_mk_le_max le_rfl
     _ = _ := by simp [max_assoc]
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis

0723536a

move(Polynomial): Move out of Data (#11751)

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

56e439ec

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2022 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.RingTheory.AlgebraicIndependent
-import Mathlib.FieldTheory.IsAlgClosed.Basic
-import Mathlib.Data.Polynomial.Cardinal
-import Mathlib.Data.MvPolynomial.Cardinal
+import Mathlib.Algebra.Polynomial.Cardinal
+import Mathlib.Algebra.MvPolynomial.Cardinal
 import Mathlib.Data.ZMod.Algebra
+import Mathlib.FieldTheory.IsAlgClosed.Basic
+import Mathlib.RingTheory.AlgebraicIndependent
 
 #align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"

0723536a

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -46,7 +46,7 @@ theorem cardinal_mk_le_sigma_polynomial :
       ⟨p.1, x, by
         dsimp
         have h : p.1.map (algebraMap R L) ≠ 0 := by
-          rw [Ne.def, ← Polynomial.degree_eq_bot,
+          rw [Ne, ← Polynomial.degree_eq_bot,
             Polynomial.degree_map_eq_of_injective (NoZeroSMulDivisors.algebraMap_injective R L),
             Polynomial.degree_eq_bot]
           exact p.2.1

0723536a

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

@@ -36,7 +36,6 @@ section AlgebraicClosure
 namespace Algebra.IsAlgebraic
 
 variable (R L : Type u) [CommRing R] [CommRing L] [IsDomain L] [Algebra R L]
-
 variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
 theorem cardinal_mk_le_sigma_polynomial :
@@ -88,15 +87,10 @@ section Classification
 noncomputable section
 
 variable {R L K : Type*} [CommRing R]
-
 variable [Field K] [Algebra R K]
-
 variable [Field L] [Algebra R L]
-
 variable {ι : Type*} (v : ι → K)
-
 variable {κ : Type*} (w : κ → L)
-
 variable (hv : AlgebraicIndependent R v)
 
 theorem isAlgClosure_of_transcendence_basis [IsAlgClosed K] (hv : IsTranscendenceBasis R v) :
@@ -132,11 +126,8 @@ end Classification
 section Cardinal
 
 variable {R L K : Type u} [CommRing R]
-
 variable [Field K] [Algebra R K] [IsAlgClosed K]
-
 variable {ι : Type u} (v : ι → K)
-
 variable (hv : IsTranscendenceBasis R v)
 
 theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :

0723536a

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -115,8 +115,8 @@ def equivOfTranscendenceBasis [IsAlgClosed K] [IsAlgClosed L] (e : ι ≃ κ)
     (hv : IsTranscendenceBasis R v) (hw : IsTranscendenceBasis R w) : K ≃+* L := by
   letI := isAlgClosure_of_transcendence_basis v hv
   letI := isAlgClosure_of_transcendence_basis w hw
-  have e : Algebra.adjoin R (Set.range v) ≃+* Algebra.adjoin R (Set.range w)
-  · refine' hv.1.aevalEquiv.symm.toRingEquiv.trans _
+  have e : Algebra.adjoin R (Set.range v) ≃+* Algebra.adjoin R (Set.range w) := by
+    refine' hv.1.aevalEquiv.symm.toRingEquiv.trans _
     refine' (AlgEquiv.ofAlgHom (MvPolynomial.rename e)
       (MvPolynomial.rename e.symm) _ _).toRingEquiv.trans _
     · ext; simp

0723536a

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

4160b2aa

Diff

@@ -55,7 +55,7 @@ theorem cardinal_mk_le_sigma_polynomial :
           p.2.2]⟩)
     fun x y => by
       intro h
-      simp at h
+      simp? at h says simp only [Set.coe_setOf, ne_eq, Set.mem_setOf_eq, Sigma.mk.inj_iff] at h
       refine' (Subtype.heq_iff_coe_eq _).1 h.2
       simp only [h.1, iff_self_iff, forall_true_iff]
 #align algebra.is_algebraic.cardinal_mk_le_sigma_polynomial Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial

0723536a

feat: roots in an algebra (#6740)

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

a57bfd63

Diff

@@ -40,8 +40,8 @@ variable (R L : Type u) [CommRing R] [CommRing L] [IsDomain L] [Algebra R L]
 variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
 theorem cardinal_mk_le_sigma_polynomial :
-    #L ≤ #(Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
-  @mk_le_of_injective L (Σ p : R[X], {x : L | x ∈ (p.map (algebraMap R L)).roots})
+    #L ≤ #(Σ p : R[X], { x : L // x ∈ p.aroots L }) :=
+  @mk_le_of_injective L (Σ p : R[X], {x : L | x ∈ p.aroots L})
     (fun x : L =>
       let p := Classical.indefiniteDescription _ (halg x)
       ⟨p.1, x, by
@@ -64,9 +64,9 @@ theorem cardinal_mk_le_sigma_polynomial :
 of the base ring or `ℵ₀` -/
 theorem cardinal_mk_le_max : #L ≤ max #R ℵ₀ :=
   calc
-    #L ≤ #(Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
+    #L ≤ #(Σ p : R[X], { x : L // x ∈ p.aroots L }) :=
       cardinal_mk_le_sigma_polynomial R L halg
-    _ = Cardinal.sum fun p : R[X] => #{x : L | x ∈ (p.map (algebraMap R L)).roots} := by
+    _ = Cardinal.sum fun p : R[X] => #{x : L | x ∈ p.aroots L} := by
       rw [← mk_sigma]; rfl
     _ ≤ Cardinal.sum.{u, u} fun _ : R[X] => ℵ₀ :=
       (sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le)

0723536a

chore: delete unused letI and nolint (#6523)

5b3ada45

Diff

@@ -207,13 +207,10 @@ private theorem ringEquivOfCardinalEqOfCharP (p : ℕ) [Fact p.Prime] [CharP K p
 
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/
-@[nolint defLemma]
 theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : ℵ₀ < #K)
     (hKL : #K = #L) : Nonempty (K ≃+* L) := by
   rcases CharP.char_is_prime_or_zero K p with (hp | hp)
   · haveI : Fact p.Prime := ⟨hp⟩
-    letI : Algebra (ZMod p) K := ZMod.algebra _ _
-    letI : Algebra (ZMod p) L := ZMod.algebra _ _
     exact ringEquivOfCardinalEqOfCharP p hK hKL
   · simp only [hp] at *
     letI : CharZero K := CharP.charP_to_charZero K

0723536a

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

@@ -87,15 +87,15 @@ section Classification
 
 noncomputable section
 
-variable {R L K : Type _} [CommRing R]
+variable {R L K : Type*} [CommRing R]
 
 variable [Field K] [Algebra R K]
 
 variable [Field L] [Algebra R L]
 
-variable {ι : Type _} (v : ι → K)
+variable {ι : Type*} (v : ι → K)
 
-variable {κ : Type _} (w : κ → L)
+variable {κ : Type*} (w : κ → L)
 
 variable (hv : AlgebraicIndependent R v)

0723536a

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.AlgebraicIndependent
 import Mathlib.FieldTheory.IsAlgClosed.Basic
@@ -14,6 +9,8 @@ import Mathlib.Data.Polynomial.Cardinal
 import Mathlib.Data.MvPolynomial.Cardinal
 import Mathlib.Data.ZMod.Algebra
 
+#align_import field_theory.is_alg_closed.classification from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
+
 /-!
 # Classification of Algebraically closed fields

0723536a

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -43,7 +43,7 @@ variable (R L : Type u) [CommRing R] [CommRing L] [IsDomain L] [Algebra R L]
 variable [NoZeroSMulDivisors R L] (halg : Algebra.IsAlgebraic R L)
 
 theorem cardinal_mk_le_sigma_polynomial :
-    (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
+    #L ≤ #(Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
   @mk_le_of_injective L (Σ p : R[X], {x : L | x ∈ (p.map (algebraMap R L)).roots})
     (fun x : L =>
       let p := Classical.indefiniteDescription _ (halg x)
@@ -65,19 +65,19 @@ theorem cardinal_mk_le_sigma_polynomial :
 
 /-- The cardinality of an algebraic extension is at most the maximum of the cardinality
 of the base ring or `ℵ₀` -/
-theorem cardinal_mk_le_max : (#L) ≤ max (#R) ℵ₀ :=
+theorem cardinal_mk_le_max : #L ≤ max #R ℵ₀ :=
   calc
-    (#L) ≤ (#Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
+    #L ≤ #(Σ p : R[X], { x : L // x ∈ (p.map (algebraMap R L)).roots }) :=
       cardinal_mk_le_sigma_polynomial R L halg
     _ = Cardinal.sum fun p : R[X] => #{x : L | x ∈ (p.map (algebraMap R L)).roots} := by
       rw [← mk_sigma]; rfl
     _ ≤ Cardinal.sum.{u, u} fun _ : R[X] => ℵ₀ :=
       (sum_le_sum _ _ fun p => (Multiset.finite_toSet _).lt_aleph0.le)
-    _ = (#R[X]) * ℵ₀ := (sum_const' _ _)
-    _ ≤ max (max (#R[X]) ℵ₀) ℵ₀ := (mul_le_max _ _)
-    _ ≤ max (max (max (#R) ℵ₀) ℵ₀) ℵ₀ :=
+    _ = #(R[X]) * ℵ₀ := (sum_const' _ _)
+    _ ≤ max (max #(R[X]) ℵ₀) ℵ₀ := (mul_le_max _ _)
+    _ ≤ max (max (max #R ℵ₀) ℵ₀) ℵ₀ :=
       (max_le_max (max_le_max Polynomial.cardinal_mk_le_max le_rfl) le_rfl)
-    _ = max (#R) ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
+    _ = max #R ℵ₀ := by simp only [max_assoc, max_comm ℵ₀, max_left_comm ℵ₀, max_self]
 #align algebra.is_algebraic.cardinal_mk_le_max Algebra.IsAlgebraic.cardinal_mk_le_max
 
 end Algebra.IsAlgebraic
@@ -143,28 +143,28 @@ variable {ι : Type u} (v : ι → K)
 variable (hv : IsTranscendenceBasis R v)
 
 theorem cardinal_le_max_transcendence_basis (hv : IsTranscendenceBasis R v) :
-    (#K) ≤ max (max (#R) (#ι)) ℵ₀ :=
+    #K ≤ max (max #R #ι) ℵ₀ :=
   calc
-    (#K) ≤ max (#Algebra.adjoin R (Set.range v)) ℵ₀ :=
+    #K ≤ max #(Algebra.adjoin R (Set.range v)) ℵ₀ :=
       letI := isAlgClosure_of_transcendence_basis v hv
       Algebra.IsAlgebraic.cardinal_mk_le_max _ _ IsAlgClosure.algebraic
-    _ = max (#MvPolynomial ι R) ℵ₀ := by rw [Cardinal.eq.2 ⟨hv.1.aevalEquiv.toEquiv⟩]
-    _ ≤ max (max (max (#R) (#ι)) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
+    _ = max #(MvPolynomial ι R) ℵ₀ := by rw [Cardinal.eq.2 ⟨hv.1.aevalEquiv.toEquiv⟩]
+    _ ≤ max (max (max #R #ι) ℵ₀) ℵ₀ := (max_le_max MvPolynomial.cardinal_mk_le_max le_rfl)
     _ = _ := by simp [max_assoc]
 #align is_alg_closed.cardinal_le_max_transcendence_basis IsAlgClosed.cardinal_le_max_transcendence_basis
 
 /-- If `K` is an uncountable algebraically closed field, then its
 cardinality is the same as that of a transcendence basis. -/
 theorem cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt [Nontrivial R]
-    (hv : IsTranscendenceBasis R v) (hR : (#R) ≤ ℵ₀) (hK : ℵ₀ < (#K)) : (#K) = (#ι) :=
-  have : ℵ₀ ≤ (#ι) := le_of_not_lt fun h => not_le_of_gt hK <|
+    (hv : IsTranscendenceBasis R v) (hR : #R ≤ ℵ₀) (hK : ℵ₀ < #K) : #K = #ι :=
+  have : ℵ₀ ≤ #ι := le_of_not_lt fun h => not_le_of_gt hK <|
     calc
-      (#K) ≤ max (max (#R) (#ι)) ℵ₀ := cardinal_le_max_transcendence_basis v hv
+      #K ≤ max (max #R #ι) ℵ₀ := cardinal_le_max_transcendence_basis v hv
       _ ≤ _ := max_le (max_le hR (le_of_lt h)) le_rfl
   le_antisymm
     (calc
-      (#K) ≤ max (max (#R) (#ι)) ℵ₀ := cardinal_le_max_transcendence_basis v hv
-      _ = (#ι) := by
+      #K ≤ max (max #R #ι) ℵ₀ := cardinal_le_max_transcendence_basis v hv
+      _ = #ι := by
         rw [max_eq_left, max_eq_right]
         · exact le_trans hR this
         · exact le_max_of_le_right this)
@@ -177,13 +177,13 @@ variable {K L : Type} [Field K] [Field L] [IsAlgClosed K] [IsAlgClosed L]
 
 /-- Two uncountable algebraically closed fields of characteristic zero are isomorphic
 if they have the same cardinality. -/
-theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
+theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ < #K)
+    (hKL : #K = #L) : Nonempty (K ≃+* L) := by
   cases' exists_isTranscendenceBasis ℤ
     (show Function.Injective (algebraMap ℤ K) from Int.cast_injective) with s hs
   cases' exists_isTranscendenceBasis ℤ
     (show Function.Injective (algebraMap ℤ L) from Int.cast_injective) with t ht
-  have : (#s) = (#t) := by
+  have : #s = #t := by
     rw [← cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt _ hs (le_of_eq mk_int) hK, ←
       cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt _ ht (le_of_eq mk_int), hKL]
     rwa [← hKL]
@@ -192,14 +192,14 @@ theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ <
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_zero IsAlgClosed.ringEquivOfCardinalEqOfCharZero
 
 private theorem ringEquivOfCardinalEqOfCharP (p : ℕ) [Fact p.Prime] [CharP K p] [CharP L p]
-    (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
+    (hK : ℵ₀ < #K) (hKL : #K = #L) : Nonempty (K ≃+* L) := by
   letI : Algebra (ZMod p) K := ZMod.algebra _ _
   letI : Algebra (ZMod p) L := ZMod.algebra _ _
   cases' exists_isTranscendenceBasis (ZMod p)
     (show Function.Injective (algebraMap (ZMod p) K) from RingHom.injective _) with s hs
   cases' exists_isTranscendenceBasis (ZMod p)
     (show Function.Injective (algebraMap (ZMod p) L) from RingHom.injective _) with t ht
-  have : (#s) = (#t) := by
+  have : #s = #t := by
     rw [← cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt _ hs
       (lt_aleph0_of_finite (ZMod p)).le hK,
       ← cardinal_eq_cardinal_transcendence_basis_of_aleph0_lt _ ht
@@ -211,8 +211,8 @@ private theorem ringEquivOfCardinalEqOfCharP (p : ℕ) [Fact p.Prime] [CharP K p
 /-- Two uncountable algebraically closed fields are isomorphic
 if they have the same cardinality and the same characteristic. -/
 @[nolint defLemma]
-theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
+theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : ℵ₀ < #K)
+    (hKL : #K = #L) : Nonempty (K ≃+* L) := by
   rcases CharP.char_is_prime_or_zero K p with (hp | hp)
   · haveI : Fact p.Prime := ⟨hp⟩
     letI : Algebra (ZMod p) K := ZMod.algebra _ _

0723536a

forward port leanprover-community/mathlib#19197 (#5284)

aa4f7c81

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.is_alg_closed.classification
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -177,10 +177,8 @@ variable {K L : Type} [Field K] [Field L] [IsAlgClosed K] [IsAlgClosed L]
 
 /-- Two uncountable algebraically closed fields of characteristic zero are isomorphic
 if they have the same cardinality. -/
-@[nolint defLemma]
 theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : K ≃+* L := by
-  apply Classical.choice
+    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
   cases' exists_isTranscendenceBasis ℤ
     (show Function.Injective (algebraMap ℤ K) from Int.cast_injective) with s hs
   cases' exists_isTranscendenceBasis ℤ
@@ -194,8 +192,9 @@ theorem ringEquivOfCardinalEqOfCharZero [CharZero K] [CharZero L] (hK : ℵ₀ <
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_zero IsAlgClosed.ringEquivOfCardinalEqOfCharZero
 
 private theorem ringEquivOfCardinalEqOfCharP (p : ℕ) [Fact p.Prime] [CharP K p] [CharP L p]
-    (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : K ≃+* L := by
-  apply Classical.choice
+    (hK : ℵ₀ < (#K)) (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
+  letI : Algebra (ZMod p) K := ZMod.algebra _ _
+  letI : Algebra (ZMod p) L := ZMod.algebra _ _
   cases' exists_isTranscendenceBasis (ZMod p)
     (show Function.Injective (algebraMap (ZMod p) K) from RingHom.injective _) with s hs
   cases' exists_isTranscendenceBasis (ZMod p)
@@ -213,15 +212,16 @@ private theorem ringEquivOfCardinalEqOfCharP (p : ℕ) [Fact p.Prime] [CharP K p
 if they have the same cardinality and the same characteristic. -/
 @[nolint defLemma]
 theorem ringEquivOfCardinalEqOfCharEq (p : ℕ) [CharP K p] [CharP L p] (hK : ℵ₀ < (#K))
-    (hKL : (#K) = (#L)) : K ≃+* L := by
-  apply Classical.choice
+    (hKL : (#K) = (#L)) : Nonempty (K ≃+* L) := by
   rcases CharP.char_is_prime_or_zero K p with (hp | hp)
   · haveI : Fact p.Prime := ⟨hp⟩
-    exact ⟨ringEquivOfCardinalEqOfCharP p hK hKL⟩
+    letI : Algebra (ZMod p) K := ZMod.algebra _ _
+    letI : Algebra (ZMod p) L := ZMod.algebra _ _
+    exact ringEquivOfCardinalEqOfCharP p hK hKL
   · simp only [hp] at *
     letI : CharZero K := CharP.charP_to_charZero K
     letI : CharZero L := CharP.charP_to_charZero L
-    exact ⟨ringEquivOfCardinalEqOfCharZero hK hKL⟩
+    exact ringEquivOfCardinalEqOfCharZero hK hKL
 #align is_alg_closed.ring_equiv_of_cardinal_eq_of_char_eq IsAlgClosed.ringEquivOfCardinalEqOfCharEq
 
 end IsAlgClosed

70fd9563

feat: port FieldTheory.IsAlgClosed.Classification (#4940)

71f13844

`field_theory.is_alg_closed.classification` ⟷ `Mathlib.FieldTheory.IsAlgClosed.Classification`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 668

field_theory.is_alg_closed.classification ⟷ Mathlib.FieldTheory.IsAlgClosed.Classification

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 668

`field_theory.is_alg_closed.classification` ⟷ `Mathlib.FieldTheory.IsAlgClosed.Classification`