number_theory.kummer_dedekind ⟷ Mathlib.NumberTheory.KummerDedekind

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

@@ -115,9 +115,9 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
     (hp : p ∈ Ideal.comap (algebraMap R S) (conductor R x)) (hz' : z ∈ I.map (algebraMap R S)) :
     algebraMap R S p * z ∈ algebraMap R<x> S '' ↑(I.map (algebraMap R R<x>)) :=
   by
-  rw [Ideal.map, Ideal.span, Finsupp.mem_span_image_iff_total] at hz' 
+  rw [Ideal.map, Ideal.span, Finsupp.mem_span_image_iff_total] at hz'
   obtain ⟨l, H, H'⟩ := hz'
-  rw [Finsupp.total_apply] at H' 
+  rw [Finsupp.total_apply] at H'
   rw [← H', mul_comm, Finsupp.sum_mul]
   have lem :
     ∀ {a : R},
@@ -172,7 +172,7 @@ theorem comap_map_eq_map_adjoin_of_coprime_conductor
       obtain ⟨a, ha⟩ :=
         (Set.mem_image _ _ _).mp
           (prod_mem_ideal_map_of_mem_conductor hp
-            (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy ))
+            (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy))
       use a + algebraMap R R<x> q * ⟨z, hz⟩
       refine'
         ⟨Ideal.add_mem (I.map (algebraMap R R<x>)) ha.left _, by
@@ -212,7 +212,7 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
         --this is contained in `I * R<x>`, which is the content of the previous lemma.
         refine' RingHom.lift_injective_of_ker_le_ideal _ _ fun u hu => _
         rwa [RingHom.mem_ker, RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem, ← Ideal.mem_comap,
-          comap_map_eq_map_adjoin_of_coprime_conductor hx h_alg] at hu 
+          comap_map_eq_map_adjoin_of_coprime_conductor hx h_alg] at hu
       · -- Surjectivity follows from the surjectivity of the canonical map `R<x> → S ⧸ (I * S)`,
         -- which in turn follows from the fact that `I * S + (conductor R x) = S`.
         refine' Ideal.Quotient.lift_surjective_of_surjective _ _ fun y => _
@@ -222,14 +222,14 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
           suffices conductor R x ⊔ I.map (algebraMap R S) = ⊤ by simp only [this]
           rw [Ideal.eq_top_iff_one] at hx ⊢
           replace hx := Ideal.mem_map_of_mem (algebraMap R S) hx
-          rw [Ideal.map_sup, RingHom.map_one] at hx 
+          rw [Ideal.map_sup, RingHom.map_one] at hx
           exact
             (sup_le_sup
                 (show ((conductor R x).comap (algebraMap R S)).map (algebraMap R S) ≤ conductor R x
                   from Ideal.map_comap_le)
                 (le_refl (I.map (algebraMap R S))))
               hx
-        rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this 
+        rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this
         obtain ⟨u, hu, hu'⟩ := this
         use⟨u, conductor_subset_adjoin hu⟩
         simpa only [← hu']
@@ -334,7 +334,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   have := multiplicity_factors_map_eq_multiplicity hI hI' hx hx' hJ
   rw [multiplicity_eq_count_normalized_factors, multiplicity_eq_count_normalized_factors,
     UniqueFactorizationMonoid.normalize_normalized_factor _ hJ,
-    UniqueFactorizationMonoid.normalize_normalized_factor, PartENat.natCast_inj] at this 
+    UniqueFactorizationMonoid.normalize_normalized_factor, PartENat.natCast_inj] at this
   refine' this.trans _
   -- Get rid of the `map` by applying the equiv to both sides.
   generalize hJ' :
@@ -381,7 +381,7 @@ theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I
         (show I.map (algebraMap R S) ≠ 0 by
           rwa [← bot_eq_zero, Ne.def,
             map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)])
-    rw [associated_iff_eq, hy, Multiset.prod_singleton] at h 
+    rw [associated_iff_eq, hy, Multiset.prod_singleton] at h
     rw [← h]
     exact
       irreducible_of_normalized_factor y

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

@@ -6,7 +6,7 @@ Authors: Anne Baanen, Paul Lezeau
 import RingTheory.DedekindDomain.Ideal
 import RingTheory.IsAdjoinRoot
 
-#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"65a1391a0106c9204fe45bc73a039f056558cb83"
 
 /-!
 # Kummer-Dedekind theorem
@@ -349,7 +349,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   rw [Multiset.count_map_eq_count' fun f =>
       ((normalized_factors_map_equiv_normalized_factors_min_poly_mk hI hI' hx hx').symm f :
         Ideal S),
-    Multiset.attach_count_eq_count_coe]
+    Multiset.count_attach]
   · exact subtype.coe_injective.comp (Equiv.injective _)
   · exact (normalized_factors_map_equiv_normalized_factors_min_poly_mk hI hI' hx hx' _).Prop
   ·

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Paul Lezeau
 -/
-import Mathbin.RingTheory.DedekindDomain.Ideal
-import Mathbin.RingTheory.IsAdjoinRoot
+import RingTheory.DedekindDomain.Ideal
+import RingTheory.IsAdjoinRoot
 
 #align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -231,7 +231,7 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
               hx
         rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this 
         obtain ⟨u, hu, hu'⟩ := this
-        use ⟨u, conductor_subset_adjoin hu⟩
+        use⟨u, conductor_subset_adjoin hu⟩
         simpa only [← hu']
         · exact Ideal.Quotient.mk_surjective)
 #align quot_adjoin_equiv_quot_map quotAdjoinEquivQuotMap
@@ -387,12 +387,11 @@ theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I
       irreducible_of_normalized_factor y
         (show y ∈ normalized_factors (I.map (algebraMap R S)) by simp [hy])
   rw [normalized_factors_ideal_map_eq_normalized_factors_min_poly_mk_map hI hI' hx hx']
-  use
-    ((normalized_factors_map_equiv_normalized_factors_min_poly_mk hI hI' hx hx').symm
+  use((normalized_factors_map_equiv_normalized_factors_min_poly_mk hI hI' hx hx').symm
         ⟨normalize (map I.Quotient.mk (minpoly R x)), mem_norm_factors⟩ :
       Ideal S)
   rw [Multiset.map_eq_singleton]
-  use ⟨normalize (map I.Quotient.mk (minpoly R x)), mem_norm_factors⟩
+  use⟨normalize (map I.Quotient.mk (minpoly R x)), mem_norm_factors⟩
   refine' ⟨_, rfl⟩
   apply Multiset.map_injective Subtype.coe_injective
   rw [Multiset.attach_map_val, Multiset.map_singleton, Subtype.coe_mk]

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Paul Lezeau
-
-! This file was ported from Lean 3 source module number_theory.kummer_dedekind
-! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.DedekindDomain.Ideal
 import Mathbin.RingTheory.IsAdjoinRoot
 
+#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+
 /-!
 # Kummer-Dedekind theorem
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -275,12 +275,10 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
                 (by
                   apply NoZeroSMulDivisors.algebraMap_injective (Algebra.adjoin R {x}) S
                   exact Subalgebra.noZeroSMulDivisors_top (Algebra.adjoin R {x}))).symm.trans
-          (((minpoly.Algebra.adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap
-                  I).toRingEquiv.trans
+          (((Algebra.adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap I).toRingEquiv.trans
             (quotEquivOfEq
               (show
-                Ideal.span
-                    {(minpoly R (minpoly.Algebra.adjoin.powerBasis' hx').gen).map I.Quotient.mk} =
+                Ideal.span {(minpoly R (Algebra.adjoin.powerBasis' hx').gen).map I.Quotient.mk} =
                   Ideal.span {(minpoly R x).map I.Quotient.mk}
                 by rw [Algebra.adjoin.powerBasis'_minpoly_gen hx']))))
         (--show that `I * S` ≠ ⊥

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Paul Lezeau
 
 ! This file was ported from Lean 3 source module number_theory.kummer_dedekind
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.IsAdjoinRoot
 /-!
 # Kummer-Dedekind theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the monogenic version of the Kummer-Dedekind theorem on the splitting of prime
 ideals in an extension of the ring of integers. This states that if `I` is a prime ideal of
 Dedekind domain `R` and `S = R[α]` for some `α` that is integral over `R` with minimal polynomial

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

@@ -62,6 +62,7 @@ open Ideal Polynomial DoubleQuot UniqueFactorizationMonoid Algebra RingHom
 
 local notation:max R "<" x ">" => adjoin R ({x} : Set S)
 
+#print conductor /-
 /-- Let `S / R` be a ring extension and `x : S`, then the conductor of `R<x>` is the
     biggest ideal of `S` contained in `R<x>`. -/
 def conductor (x : S) : Ideal S
@@ -71,31 +72,43 @@ def conductor (x : S) : Ideal S
   add_mem' a b ha hb c := by simpa only [add_mul] using Subalgebra.add_mem _ (ha c) (hb c)
   smul_mem' c a ha b := by simpa only [smul_eq_mul, mul_left_comm, mul_assoc] using ha (c * b)
 #align conductor conductor
+-/
 
 variable {R} {x : S}
 
+#print conductor_eq_of_eq /-
 theorem conductor_eq_of_eq {y : S} (h : (R<x> : Set S) = R<y>) : conductor R x = conductor R y :=
   Ideal.ext fun a => forall_congr' fun b => Set.ext_iff.mp h _
 #align conductor_eq_of_eq conductor_eq_of_eq
+-/
 
+#print conductor_subset_adjoin /-
 theorem conductor_subset_adjoin : (conductor R x : Set S) ⊆ R<x> := fun y hy => by
   simpa only [mul_one] using hy 1
 #align conductor_subset_adjoin conductor_subset_adjoin
+-/
 
+#print mem_conductor_iff /-
 theorem mem_conductor_iff {y : S} : y ∈ conductor R x ↔ ∀ b : S, y * b ∈ R<x> :=
   ⟨fun h => h, fun h => h⟩
 #align mem_conductor_iff mem_conductor_iff
+-/
 
+#print conductor_eq_top_of_adjoin_eq_top /-
 theorem conductor_eq_top_of_adjoin_eq_top (h : R<x> = ⊤) : conductor R x = ⊤ := by
   simp only [Ideal.eq_top_iff_one, mem_conductor_iff, h, mem_top, forall_const]
 #align conductor_eq_top_of_adjoin_eq_top conductor_eq_top_of_adjoin_eq_top
+-/
 
+#print conductor_eq_top_of_powerBasis /-
 theorem conductor_eq_top_of_powerBasis (pb : PowerBasis R S) : conductor R pb.gen = ⊤ :=
   conductor_eq_top_of_adjoin_eq_top pb.adjoin_gen_eq_top
 #align conductor_eq_top_of_power_basis conductor_eq_top_of_powerBasis
+-/
 
 variable {I : Ideal R}
 
+#print prod_mem_ideal_map_of_mem_conductor /-
 /-- This technical lemma tell us that if `C` is the conductor of `R<x>` and `I` is an ideal of `R`
   then `p * (I * S) ⊆ I * R<x>` for any `p` in `C ∩ R` -/
 theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
@@ -133,7 +146,9 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
   · intro y hy
     exact lem ((Finsupp.mem_supported _ l).mp H hy)
 #align prod_mem_ideal_map_of_mem_conductor prod_mem_ideal_map_of_mem_conductor
+-/
 
+#print comap_map_eq_map_adjoin_of_coprime_conductor /-
 /-- A technical result telling us that `(I * S) ∩ R<x> = I * R<x>` for any ideal `I` of `R`. -/
 theorem comap_map_eq_map_adjoin_of_coprime_conductor
     (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤)
@@ -176,7 +191,9 @@ theorem comap_map_eq_map_adjoin_of_coprime_conductor
     rw [this, ← Ideal.map_map]
     apply Ideal.le_comap_map
 #align comap_map_eq_map_adjoin_of_coprime_conductor comap_map_eq_map_adjoin_of_coprime_conductor
+-/
 
+#print quotAdjoinEquivQuotMap /-
 /-- The canonical morphism of rings from `R<x> ⧸ (I*R<x>)` to `S ⧸ (I*S)` is an isomorphism
     when `I` and `(conductor R x) ∩ R` are coprime. -/
 noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤)
@@ -218,7 +235,9 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
         simpa only [← hu']
         · exact Ideal.Quotient.mk_surjective)
 #align quot_adjoin_equiv_quot_map quotAdjoinEquivQuotMap
+-/
 
+#print quotAdjoinEquivQuotMap_apply_mk /-
 @[simp]
 theorem quotAdjoinEquivQuotMap_apply_mk (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤)
     (h_alg : Function.Injective (algebraMap R<x> S)) (a : R<x>) :
@@ -226,6 +245,7 @@ theorem quotAdjoinEquivQuotMap_apply_mk (hx : (conductor R x).comap (algebraMap
       (I.map (algebraMap R S)).Quotient.mk ↑a :=
   rfl
 #align quot_adjoin_equiv_quot_map_apply_mk quotAdjoinEquivQuotMap_apply_mk
+-/
 
 namespace KummerDedekind
 
@@ -239,6 +259,7 @@ variable [NoZeroSMulDivisors R S]
 
 attribute [local instance] Ideal.Quotient.field
 
+#print KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk /-
 /-- The first half of the **Kummer-Dedekind Theorem** in the monogenic case, stating that the prime
     factors of `I*S` are in bijection with those of the minimal polynomial of the generator of `S`
     over `R`, taken `mod I`.-/
@@ -273,7 +294,9 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
         (show map I.Quotient.mk (minpoly R x) ≠ 0 from
           Polynomial.map_monic_ne_zero (minpoly.monic hx'))).symm
 #align kummer_dedekind.normalized_factors_map_equiv_normalized_factors_min_poly_mk KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk
+-/
 
+#print KummerDedekind.multiplicity_factors_map_eq_multiplicity /-
 /-- The second half of the **Kummer-Dedekind Theorem** in the monogenic case, stating that the
     bijection `factors_equiv'` defined in the first half preserves multiplicities. -/
 theorem multiplicity_factors_map_eq_multiplicity (hI : IsMaximal I) (hI' : I ≠ ⊥)
@@ -288,7 +311,9 @@ theorem multiplicity_factors_map_eq_multiplicity (hI : IsMaximal I) (hI' : I ≠
     multiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_multiplicity,
     normalizedFactorsEquivOfQuotEquiv_multiplicity_eq_multiplicity]
 #align kummer_dedekind.multiplicity_factors_map_eq_multiplicity KummerDedekind.multiplicity_factors_map_eq_multiplicity
+-/
 
+#print KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map /-
 /-- The **Kummer-Dedekind Theorem**. -/
 theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : IsMaximal I)
     (hI' : I ≠ ⊥) (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤) (hx' : IsIntegral R x) :
@@ -339,7 +364,9 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
     rwa [← bot_eq_zero, Ne.def,
       map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)]
 #align kummer_dedekind.normalized_factors_ideal_map_eq_normalized_factors_min_poly_mk_map KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map
+-/
 
+#print KummerDedekind.Ideal.irreducible_map_of_irreducible_minpoly /-
 theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I ≠ ⊥)
     (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤) (hx' : IsIntegral R x)
     (hf : Irreducible (map I.Quotient.mk (minpoly R x))) : Irreducible (I.map (algebraMap R S)) :=
@@ -373,6 +400,7 @@ theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I
   rw [Multiset.attach_map_val, Multiset.map_singleton, Subtype.coe_mk]
   exact normalized_factors_irreducible hf
 #align kummer_dedekind.ideal.irreducible_map_of_irreducible_minpoly KummerDedekind.Ideal.irreducible_map_of_irreducible_minpoly
+-/
 
 end KummerDedekind
 

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

@@ -251,10 +251,12 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
                 (by
                   apply NoZeroSMulDivisors.algebraMap_injective (Algebra.adjoin R {x}) S
                   exact Subalgebra.noZeroSMulDivisors_top (Algebra.adjoin R {x}))).symm.trans
-          (((Algebra.adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap I).toRingEquiv.trans
+          (((minpoly.Algebra.adjoin.powerBasis' hx').quotientEquivQuotientMinpolyMap
+                  I).toRingEquiv.trans
             (quotEquivOfEq
               (show
-                Ideal.span {(minpoly R (Algebra.adjoin.powerBasis' hx').gen).map I.Quotient.mk} =
+                Ideal.span
+                    {(minpoly R (minpoly.Algebra.adjoin.powerBasis' hx').gen).map I.Quotient.mk} =
                   Ideal.span {(minpoly R x).map I.Quotient.mk}
                 by rw [Algebra.adjoin.powerBasis'_minpoly_gen hx']))))
         (--show that `I * S` ≠ ⊥

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

@@ -60,7 +60,6 @@ variable (R : Type _) {S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
 open Ideal Polynomial DoubleQuot UniqueFactorizationMonoid Algebra RingHom
 
--- mathport name: «expr < >»
 local notation:max R "<" x ">" => adjoin R ({x} : Set S)
 
 /-- Let `S / R` be a ring extension and `x : S`, then the conductor of `R<x>` is the

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

@@ -67,7 +67,7 @@ local notation:max R "<" x ">" => adjoin R ({x} : Set S)
     biggest ideal of `S` contained in `R<x>`. -/
 def conductor (x : S) : Ideal S
     where
-  carrier := { a | ∀ b : S, a * b ∈ R<x> }
+  carrier := {a | ∀ b : S, a * b ∈ R<x>}
   zero_mem' b := by simpa only [MulZeroClass.zero_mul] using Subalgebra.zero_mem _
   add_mem' a b ha hb c := by simpa only [add_mul] using Subalgebra.add_mem _ (ha c) (hb c)
   smul_mem' c a ha b := by simpa only [smul_eq_mul, mul_left_comm, mul_assoc] using ha (c * b)
@@ -245,8 +245,8 @@ attribute [local instance] Ideal.Quotient.field
     over `R`, taken `mod I`.-/
 noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMaximal I)
     (hI' : I ≠ ⊥) (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤) (hx' : IsIntegral R x) :
-    { J : Ideal S | J ∈ normalizedFactors (I.map (algebraMap R S)) } ≃
-      { d : (R ⧸ I)[X] | d ∈ normalizedFactors (map I.Quotient.mk (minpoly R x)) } :=
+    {J : Ideal S | J ∈ normalizedFactors (I.map (algebraMap R S))} ≃
+      {d : (R ⧸ I)[X] | d ∈ normalizedFactors (map I.Quotient.mk (minpoly R x))} :=
   (normalizedFactorsEquivOfQuotEquiv
         ((quotAdjoinEquivQuotMap hx
                 (by

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

@@ -103,9 +103,9 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
     (hp : p ∈ Ideal.comap (algebraMap R S) (conductor R x)) (hz' : z ∈ I.map (algebraMap R S)) :
     algebraMap R S p * z ∈ algebraMap R<x> S '' ↑(I.map (algebraMap R R<x>)) :=
   by
-  rw [Ideal.map, Ideal.span, Finsupp.mem_span_image_iff_total] at hz'
+  rw [Ideal.map, Ideal.span, Finsupp.mem_span_image_iff_total] at hz' 
   obtain ⟨l, H, H'⟩ := hz'
-  rw [Finsupp.total_apply] at H'
+  rw [Finsupp.total_apply] at H' 
   rw [← H', mul_comm, Finsupp.sum_mul]
   have lem :
     ∀ {a : R},
@@ -121,7 +121,7 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
         _
     · rw [mul_comm]
       exact mem_conductor_iff.mp (ideal.mem_comap.mp hp) _
-    refine' ⟨_, by simpa only [RingHom.map_mul, mul_comm (algebraMap R S p) (l a)] ⟩
+    refine' ⟨_, by simpa only [RingHom.map_mul, mul_comm (algebraMap R S p) (l a)]⟩
     rw [mul_comm]
     apply Ideal.mul_mem_left (I.map (algebraMap R R<x>)) _ (Ideal.mem_map_of_mem _ ha)
   refine'
@@ -158,11 +158,11 @@ theorem comap_map_eq_map_adjoin_of_coprime_conductor
       obtain ⟨a, ha⟩ :=
         (Set.mem_image _ _ _).mp
           (prod_mem_ideal_map_of_mem_conductor hp
-            (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy))
+            (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy ))
       use a + algebraMap R R<x> q * ⟨z, hz⟩
       refine'
         ⟨Ideal.add_mem (I.map (algebraMap R R<x>)) ha.left _, by
-          simpa only [ha.right, map_add, AlgHom.map_mul, add_right_inj] ⟩
+          simpa only [ha.right, map_add, AlgHom.map_mul, add_right_inj]⟩
       rw [mul_comm]
       exact Ideal.mul_mem_left (I.map (algebraMap R R<x>)) _ (Ideal.mem_map_of_mem _ hq)
     refine'
@@ -196,7 +196,7 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
         --this is contained in `I * R<x>`, which is the content of the previous lemma.
         refine' RingHom.lift_injective_of_ker_le_ideal _ _ fun u hu => _
         rwa [RingHom.mem_ker, RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem, ← Ideal.mem_comap,
-          comap_map_eq_map_adjoin_of_coprime_conductor hx h_alg] at hu
+          comap_map_eq_map_adjoin_of_coprime_conductor hx h_alg] at hu 
       · -- Surjectivity follows from the surjectivity of the canonical map `R<x> → S ⧸ (I * S)`,
         -- which in turn follows from the fact that `I * S + (conductor R x) = S`.
         refine' Ideal.Quotient.lift_surjective_of_surjective _ _ fun y => _
@@ -204,16 +204,16 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
         have : z ∈ conductor R x ⊔ I.map (algebraMap R S) :=
           by
           suffices conductor R x ⊔ I.map (algebraMap R S) = ⊤ by simp only [this]
-          rw [Ideal.eq_top_iff_one] at hx⊢
+          rw [Ideal.eq_top_iff_one] at hx ⊢
           replace hx := Ideal.mem_map_of_mem (algebraMap R S) hx
-          rw [Ideal.map_sup, RingHom.map_one] at hx
+          rw [Ideal.map_sup, RingHom.map_one] at hx 
           exact
             (sup_le_sup
                 (show ((conductor R x).comap (algebraMap R S)).map (algebraMap R S) ≤ conductor R x
                   from Ideal.map_comap_le)
                 (le_refl (I.map (algebraMap R S))))
               hx
-        rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this
+        rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this 
         obtain ⟨u, hu, hu'⟩ := this
         use ⟨u, conductor_subset_adjoin hu⟩
         simpa only [← hu']
@@ -310,7 +310,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   have := multiplicity_factors_map_eq_multiplicity hI hI' hx hx' hJ
   rw [multiplicity_eq_count_normalized_factors, multiplicity_eq_count_normalized_factors,
     UniqueFactorizationMonoid.normalize_normalized_factor _ hJ,
-    UniqueFactorizationMonoid.normalize_normalized_factor, PartENat.natCast_inj] at this
+    UniqueFactorizationMonoid.normalize_normalized_factor, PartENat.natCast_inj] at this 
   refine' this.trans _
   -- Get rid of the `map` by applying the equiv to both sides.
   generalize hJ' :
@@ -355,7 +355,7 @@ theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I
         (show I.map (algebraMap R S) ≠ 0 by
           rwa [← bot_eq_zero, Ne.def,
             map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)])
-    rw [associated_iff_eq, hy, Multiset.prod_singleton] at h
+    rw [associated_iff_eq, hy, Multiset.prod_singleton] at h 
     rw [← h]
     exact
       irreducible_of_normalized_factor y

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

@@ -230,7 +230,7 @@ theorem quotAdjoinEquivQuotMap_apply_mk (hx : (conductor R x).comap (algebraMap
 
 namespace KummerDedekind
 
-open BigOperators Polynomial Classical
+open scoped BigOperators Polynomial Classical
 
 variable [IsDomain R] [IsIntegrallyClosed R]
 

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

@@ -173,10 +173,7 @@ theorem comap_map_eq_map_adjoin_of_coprime_conductor
         simpa [hx₂]
       rwa [← this]
   · -- The converse inclusion is trivial
-    have : algebraMap R S = (algebraMap _ S).comp (algebraMap R R<x>) :=
-      by
-      ext
-      rfl
+    have : algebraMap R S = (algebraMap _ S).comp (algebraMap R R<x>) := by ext; rfl
     rw [this, ← Ideal.map_map]
     apply Ideal.le_comap_map
 #align comap_map_eq_map_adjoin_of_coprime_conductor comap_map_eq_map_adjoin_of_coprime_conductor
@@ -190,10 +187,7 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
     (Ideal.Quotient.lift (I.map (algebraMap R R<x>))
       ((I.map (algebraMap R S)).Quotient.mk.comp (algebraMap R<x> S)) fun r hr =>
       by
-      have : algebraMap R S = (algebraMap R<x> S).comp (algebraMap R R<x>) :=
-        by
-        ext
-        rfl
+      have : algebraMap R S = (algebraMap R<x> S).comp (algebraMap R R<x>) := by ext; rfl
       rw [RingHom.comp_apply, Ideal.Quotient.eq_zero_iff_mem, this, ← Ideal.map_map]
       exact Ideal.mem_map_of_mem _ hr)
     (by
@@ -269,8 +263,7 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
           rwa [Ne.def, map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S), ←
             Ne.def])
         (--show that the ideal spanned by `(minpoly R pb.gen) mod I` is non-zero
-        by
-          by_contra
+        by by_contra;
           exact
             (show map I.Quotient.mk (minpoly R x) ≠ 0 from
                 Polynomial.map_monic_ne_zero (minpoly.monic hx'))
@@ -306,7 +299,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   by
   ext J
   -- WLOG, assume J is a normalized factor
-  by_cases hJ : J ∈ normalized_factors (I.map (algebraMap R S))
+  by_cases hJ : J ∈ normalized_factors (I.map (algebraMap R S));
   swap
   · rw [multiset.count_eq_zero.mpr hJ, eq_comm, Multiset.count_eq_zero, Multiset.mem_map]
     simp only [Multiset.mem_attach, true_and_iff, not_exists]

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

@@ -4,11 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Paul Lezeau
 
 ! This file was ported from Lean 3 source module number_theory.kummer_dedekind
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.RingTheory.AlgebraTower
 import Mathbin.RingTheory.DedekindDomain.Ideal
 import Mathbin.RingTheory.IsAdjoinRoot
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -69,7 +69,7 @@ local notation:max R "<" x ">" => adjoin R ({x} : Set S)
 def conductor (x : S) : Ideal S
     where
   carrier := { a | ∀ b : S, a * b ∈ R<x> }
-  zero_mem' b := by simpa only [zero_mul] using Subalgebra.zero_mem _
+  zero_mem' b := by simpa only [MulZeroClass.zero_mul] using Subalgebra.zero_mem _
   add_mem' a b ha hb c := by simpa only [add_mul] using Subalgebra.add_mem _ (ha c) (hb c)
   smul_mem' c a ha b := by simpa only [smul_eq_mul, mul_left_comm, mul_assoc] using ha (c * b)
 #align conductor conductor

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

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

@@ -140,9 +140,9 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
         rfl
   refine Finset.sum_induction _ (fun u => u ∈ algebraMap R<x> S '' I.map (algebraMap R R<x>))
       (fun a b => ?_) ?_ ?_
-  rintro ⟨z, hz, rfl⟩ ⟨y, hy, rfl⟩
-  rw [← RingHom.map_add]
-  exact ⟨z + y, Ideal.add_mem _ (SetLike.mem_coe.mp hz) hy, rfl⟩
+  · rintro ⟨z, hz, rfl⟩ ⟨y, hy, rfl⟩
+    rw [← RingHom.map_add]
+    exact ⟨z + y, Ideal.add_mem _ (SetLike.mem_coe.mp hz) hy, rfl⟩
   · exact ⟨0, SetLike.mem_coe.mpr <| Ideal.zero_mem _, RingHom.map_zero _⟩
   · intro y hy
     exact lem ((Finsupp.mem_supported _ l).mp H hy)
@@ -217,10 +217,10 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
           from Ideal.map_comap_le)
           (le_refl (I.map (algebraMap R S)))) hx
     rw [← Ideal.mem_quotient_iff_mem_sup, hz, Ideal.mem_map_iff_of_surjective] at this
-    obtain ⟨u, hu, hu'⟩ := this
-    use ⟨u, conductor_subset_adjoin hu⟩
-    simp only [← hu']
-    rfl
+    · obtain ⟨u, hu, hu'⟩ := this
+      use ⟨u, conductor_subset_adjoin hu⟩
+      simp only [← hu']
+      rfl
     · exact Ideal.Quotient.mk_surjective
 #align quot_adjoin_equiv_quot_map quotAdjoinEquivQuotMap
 
@@ -304,20 +304,20 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   rw [multiplicity_eq_count_normalizedFactors, multiplicity_eq_count_normalizedFactors,
     UniqueFactorizationMonoid.normalize_normalized_factor _ hJ,
     UniqueFactorizationMonoid.normalize_normalized_factor, PartENat.natCast_inj] at this
-  refine' this.trans _
-  -- Get rid of the `map` by applying the equiv to both sides.
-  generalize hJ' :
-    (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx') ⟨J, hJ⟩ = J'
-  have : ((normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx').symm J' : Ideal S) =
-      J :=
-    by rw [← hJ', Equiv.symm_apply_apply _ _, Subtype.coe_mk]
-  subst this
-  -- Get rid of the `attach` by applying the subtype `coe` to both sides.
-  rw [Multiset.count_map_eq_count' fun f =>
-      ((normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx').symm f :
-        Ideal S),
-    Multiset.count_attach]
-  · exact Subtype.coe_injective.comp (Equiv.injective _)
+  · refine' this.trans _
+    -- Get rid of the `map` by applying the equiv to both sides.
+    generalize hJ' :
+      (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx') ⟨J, hJ⟩ = J'
+    have : ((normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx').symm J' : Ideal S) =
+        J :=
+      by rw [← hJ', Equiv.symm_apply_apply _ _, Subtype.coe_mk]
+    subst this
+    -- Get rid of the `attach` by applying the subtype `coe` to both sides.
+    rw [Multiset.count_map_eq_count' fun f =>
+        ((normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx').symm f :
+          Ideal S),
+      Multiset.count_attach]
+    · exact Subtype.coe_injective.comp (Equiv.injective _)
   · exact (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx' _).prop
   · exact irreducible_of_normalized_factor _
         (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx' _).prop

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -261,8 +261,7 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
     · exact NoZeroSMulDivisors.algebraMap_injective (Algebra.adjoin R {x}) S
     · rw [Algebra.adjoin.powerBasis'_minpoly_gen hx']
   refine (normalizedFactorsEquivOfQuotEquiv f ?_ ?_).trans ?_
-  · rwa [Ne.def, map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S),
-      ← Ne.def]
+  · rwa [Ne, map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S), ← Ne]
   · by_contra h
     exact (show Polynomial.map (Ideal.Quotient.mk I) (minpoly R x) ≠ 0 from
       Polynomial.map_monic_ne_zero (minpoly.monic hx')) (span_singleton_eq_bot.mp h)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -245,7 +245,7 @@ attribute [local instance] Ideal.Quotient.field
 
 /-- The first half of the **Kummer-Dedekind Theorem** in the monogenic case, stating that the prime
     factors of `I*S` are in bijection with those of the minimal polynomial of the generator of `S`
-    over `R`, taken `mod I`.-/
+    over `R`, taken `mod I`. -/
 noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMaximal I)
     (hI' : I ≠ ⊥) (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤) (hx' : IsIntegral R x) :
     {J : Ideal S | J ∈ normalizedFactors (I.map (algebraMap R S))} ≃

@@ -324,7 +324,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
         (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx' _).prop
   · exact Polynomial.map_monic_ne_zero (minpoly.monic hx')
   · exact irreducible_of_normalized_factor _ hJ
-  · rwa [← bot_eq_zero, Ne.def,
+  · rwa [← bot_eq_zero, Ne,
       map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)]
 #align kummer_dedekind.normalized_factors_ideal_map_eq_normalized_factors_min_poly_mk_map KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map
 
@@ -338,7 +338,7 @@ theorem Ideal.irreducible_map_of_irreducible_minpoly (hI : IsMaximal I) (hI' : I
   suffices ∃ y, normalizedFactors (I.map (algebraMap R S)) = {y} by
     obtain ⟨y, hy⟩ := this
     have h := normalizedFactors_prod (show I.map (algebraMap R S) ≠ 0 by
-          rwa [← bot_eq_zero, Ne.def,
+          rwa [← bot_eq_zero, Ne,
             map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)])
     rw [associated_iff_eq, hy, Multiset.prod_singleton] at h
     rw [← h]

Probably because in mathlib4 the definition IsDedekindDomain extends Domain, and this was not the case in mathlib3, there are unused hypothesis of the form

variable [IsDomain R] [IsDedekindDomain R]

and this PR removes the first one, that can be inferred by the second, both in variable declarations and in theorem/definition assumptions. A regex search has been performed on the library to search for all occurrences and none is left.

@@ -238,7 +238,7 @@ namespace KummerDedekind
 open scoped BigOperators Polynomial Classical
 
 variable [IsDomain R] [IsIntegrallyClosed R]
-variable [IsDomain S] [IsDedekindDomain S]
+variable [IsDedekindDomain S]
 variable [NoZeroSMulDivisors R S]
 
 attribute [local instance] Ideal.Quotient.field

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)

@@ -238,9 +238,7 @@ namespace KummerDedekind
 open scoped BigOperators Polynomial Classical
 
 variable [IsDomain R] [IsIntegrallyClosed R]
-
 variable [IsDomain S] [IsDedekindDomain S]
-
 variable [NoZeroSMulDivisors R S]
 
 attribute [local instance] Ideal.Quotient.field

@@ -90,6 +90,28 @@ theorem conductor_eq_top_of_powerBasis (pb : PowerBasis R S) : conductor R pb.ge
   conductor_eq_top_of_adjoin_eq_top pb.adjoin_gen_eq_top
 #align conductor_eq_top_of_power_basis conductor_eq_top_of_powerBasis
 
+open IsLocalization in
+lemma mem_coeSubmodule_conductor {L} [CommRing L] [Algebra S L] [Algebra R L]
+    [IsScalarTower R S L] [NoZeroSMulDivisors S L] {x : S} {y : L} :
+    y ∈ coeSubmodule L (conductor R x) ↔ ∀ z : S,
+      y * (algebraMap S L) z ∈ Algebra.adjoin R {algebraMap S L x} := by
+  cases subsingleton_or_nontrivial L
+  · rw [Subsingleton.elim (coeSubmodule L _) ⊤, Subsingleton.elim (Algebra.adjoin R _) ⊤]; simp
+  trans ∀ z, y * (algebraMap S L) z ∈ (Algebra.adjoin R {x}).map (IsScalarTower.toAlgHom R S L)
+  · simp only [coeSubmodule, Submodule.mem_map, Algebra.linearMap_apply, Subalgebra.mem_map,
+      IsScalarTower.coe_toAlgHom']
+    constructor
+    · rintro ⟨y, hy, rfl⟩ z
+      exact ⟨_, hy z, map_mul _ _ _⟩
+    · intro H
+      obtain ⟨y, _, e⟩ := H 1
+      rw [_root_.map_one, mul_one] at e
+      subst e
+      simp only [← _root_.map_mul, (NoZeroSMulDivisors.algebraMap_injective S L).eq_iff,
+        exists_eq_right] at H
+      exact ⟨_, H, rfl⟩
+  · rw [AlgHom.map_adjoin, Set.image_singleton]; rfl
+
 variable {I : Ideal R}
 
 /-- This technical lemma tell us that if `C` is the conductor of `R<x>` and `I` is an ideal of `R`

Match https://github.com/leanprover-community/mathlib/pull/18087

@@ -6,7 +6,7 @@ Authors: Anne Baanen, Paul Lezeau
 import Mathlib.RingTheory.DedekindDomain.Ideal
 import Mathlib.RingTheory.IsAdjoinRoot
 
-#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"65a1391a0106c9204fe45bc73a039f056558cb83"
 
 /-!
 # Kummer-Dedekind theorem
@@ -297,7 +297,7 @@ theorem normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map (hI : I
   rw [Multiset.count_map_eq_count' fun f =>
       ((normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx').symm f :
         Ideal S),
-    Multiset.attach_count_eq_count_coe]
+    Multiset.count_attach]
   · exact Subtype.coe_injective.comp (Equiv.injective _)
   · exact (normalizedFactorsMapEquivNormalizedFactorsMinPolyMk hI hI' hx hx' _).prop
   · exact irreducible_of_normalized_factor _

Purely cosmetic PR.

@@ -144,7 +144,7 @@ theorem comap_map_eq_map_adjoin_of_coprime_conductor
         (⟨z, hz⟩ : R<x>) ∈ I.map (algebraMap R R<x>) by
       rw [← this, ← temp]
       obtain ⟨a, ha⟩ := (Set.mem_image _ _ _).mp (prod_mem_ideal_map_of_mem_conductor hp
-          (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy ))
+          (show z ∈ I.map (algebraMap R S) by rwa [Ideal.mem_comap] at hy))
       use a + algebraMap R R<x> q * ⟨z, hz⟩
       refine ⟨Ideal.add_mem (I.map (algebraMap R R<x>)) ha.left ?_, by
           simp only [ha.right, map_add, AlgHom.map_mul, add_right_inj]; rfl⟩

This rolls in the changed from #6928.

Co-authored-by: Thomas Murrills <thomasmurrills@gmail.com>

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

@@ -107,10 +107,11 @@ theorem prod_mem_ideal_map_of_mem_conductor {p : R} {z : S}
     rw [Algebra.id.smul_eq_mul, mul_assoc, mul_comm, mul_assoc, Set.mem_image]
     refine Exists.intro
         (algebraMap R R<x> a * ⟨l a * algebraMap R S p,
-          show l a * algebraMap R S p ∈ R<x> from ?_⟩) ?_
+          show l a * algebraMap R S p ∈ R<x> from ?h⟩) ?_
+    case h =>
+      rw [mul_comm]
+      exact mem_conductor_iff.mp (Ideal.mem_comap.mp hp) _
     · refine ⟨?_, ?_⟩
-      · rw [mul_comm]
-        exact mem_conductor_iff.mp (Ideal.mem_comap.mp hp) _
       · rw [mul_comm]
         apply Ideal.mul_mem_left (I.map (algebraMap R R<x>)) _ (Ideal.mem_map_of_mem _ ha)
       · simp only [RingHom.map_mul, mul_comm (algebraMap R S p) (l a)]

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).

@@ -63,7 +63,7 @@ local notation:max R "<" x:max ">" => adjoin R ({x} : Set S)
     biggest ideal of `S` contained in `R<x>`. -/
 def conductor (x : S) : Ideal S where
   carrier := {a | ∀ b : S, a * b ∈ R<x>}
-  zero_mem' b := by simpa only [MulZeroClass.zero_mul] using Subalgebra.zero_mem _
+  zero_mem' b := by simpa only [zero_mul] using Subalgebra.zero_mem _
   add_mem' ha hb c := by simpa only [add_mul] using Subalgebra.add_mem _ (ha c) (hb c)
   smul_mem' c a ha b := by simpa only [smul_eq_mul, mul_left_comm, mul_assoc] using ha (c * b)
 #align conductor conductor

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

This has nice performance benefits.

@@ -53,7 +53,7 @@ kummer, dedekind, kummer dedekind, dedekind-kummer, dedekind kummer
 -/
 
 
-variable (R : Type _) {S : Type _} [CommRing R] [CommRing S] [Algebra R S]
+variable (R : Type*) {S : Type*} [CommRing R] [CommRing S] [Algebra R S]
 
 open Ideal Polynomial DoubleQuot UniqueFactorizationMonoid Algebra RingHom
 

• 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 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Paul Lezeau
-
-! This file was ported from Lean 3 source module number_theory.kummer_dedekind
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.DedekindDomain.Ideal
 import Mathlib.RingTheory.IsAdjoinRoot
 
+#align_import number_theory.kummer_dedekind from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Kummer-Dedekind theorem
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -248,7 +248,7 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
   · by_contra h
     exact (show Polynomial.map (Ideal.Quotient.mk I) (minpoly R x) ≠ 0 from
       Polynomial.map_monic_ne_zero (minpoly.monic hx')) (span_singleton_eq_bot.mp h)
-  · refine (normalizedFactorsEquivSpanNormalizedFactors  ?_).symm
+  · refine (normalizedFactorsEquivSpanNormalizedFactors ?_).symm
     exact Polynomial.map_monic_ne_zero (minpoly.monic hx')
 #align kummer_dedekind.normalized_factors_map_equiv_normalized_factors_min_poly_mk KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk
 

These are the mathlib3 names.

@@ -204,7 +204,7 @@ noncomputable def quotAdjoinEquivQuotMap (hx : (conductor R x).comap (algebraMap
     · exact Ideal.Quotient.mk_surjective
 #align quot_adjoin_equiv_quot_map quotAdjoinEquivQuotMap
 
--- Porting note: on-line linter fails with `failed to synthesize` instance 
+-- Porting note: on-line linter fails with `failed to synthesize` instance
 -- but #lint does not report any problem
 @[simp, nolint simpNF]
 theorem quotAdjoinEquivQuotMap_apply_mk (hx : (conductor R x).comap (algebraMap R S) ⊔ I = ⊤)
@@ -238,7 +238,7 @@ noncomputable def normalizedFactorsMapEquivNormalizedFactorsMinPolyMk (hI : IsMa
   let f : S ⧸ map (algebraMap R S) I ≃+*
     (R ⧸ I)[X] ⧸ span {Polynomial.map (Ideal.Quotient.mk I) (minpoly R x)} := by
     refine (quotAdjoinEquivQuotMap hx ?_).symm.trans
-      (((minpoly.Algebra.adjoin.powerBasis'
+      (((Algebra.adjoin.powerBasis'
         hx').quotientEquivQuotientMinpolyMap I).toRingEquiv.trans (quotEquivOfEq ?_))
     · exact NoZeroSMulDivisors.algebraMap_injective (Algebra.adjoin R {x}) S
     · rw [Algebra.adjoin.powerBasis'_minpoly_gen hx']