ring_theory.dedekind_domain.dvr ⟷ Mathlib.RingTheory.DedekindDomain.Dvr

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

@@ -5,7 +5,7 @@ Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
 -/
 import RingTheory.Localization.LocalizationLocalization
 import RingTheory.Localization.Submodule
-import RingTheory.DiscreteValuationRing.Tfae
+import RingTheory.DiscreteValuationRing.TFAE
 
 #align_import ring_theory.dedekind_domain.dvr from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 
@@ -55,7 +55,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 open scoped nonZeroDivisors Polynomial
 
 #print IsDedekindDomainDvr /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
 

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

@@ -82,7 +82,7 @@ theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing
   intro p hp0 hpp
   refine' ideal.is_maximal_def.mpr ⟨hpp.ne_top, Ideal.maximal_of_no_maximal fun P hpP hPm => _⟩
   have hpP' : (⟨p, hpp⟩ : { p : Ideal Rₘ // p.IsPrime }) < ⟨P, hPm.is_prime⟩ := hpP
-  rw [← (IsLocalization.orderIsoOfPrime M Rₘ).lt_iff_lt] at hpP' 
+  rw [← (IsLocalization.orderIsoOfPrime M Rₘ).lt_iff_lt] at hpP'
   haveI : Ideal.IsPrime (Ideal.comap (algebraMap R Rₘ) p) :=
     ((IsLocalization.orderIsoOfPrime M Rₘ) ⟨p, hpp⟩).2.1
   haveI : Ideal.IsPrime (Ideal.comap (algebraMap R Rₘ) P) :=

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

@@ -151,7 +151,15 @@ theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP :
 /-- In a Dedekind domain, the localization at every nonzero prime ideal is a DVR. -/
 theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedekindDomain A]
     {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ]
-    [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by classical
+    [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
+  classical
+  letI : IsNoetherianRing Aₘ :=
+    IsLocalization.isNoetherianRing P.prime_compl _ IsDedekindDomain.isNoetherianRing
+  letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
+  have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
+  exact
+    ((DiscreteValuationRing.TFAE Aₘ hnf).out 0 2).mpr
+      (IsLocalization.AtPrime.isDedekindDomain A P _)
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
 -/
 

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

@@ -151,15 +151,7 @@ theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP :
 /-- In a Dedekind domain, the localization at every nonzero prime ideal is a DVR. -/
 theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedekindDomain A]
     {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ]
-    [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
-  classical
-  letI : IsNoetherianRing Aₘ :=
-    IsLocalization.isNoetherianRing P.prime_compl _ IsDedekindDomain.isNoetherianRing
-  letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
-  have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
-  exact
-    ((DiscreteValuationRing.TFAE Aₘ hnf).out 0 2).mpr
-      (IsLocalization.AtPrime.isDedekindDomain A P _)
+    [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by classical
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
 -/
-import Mathbin.RingTheory.Localization.LocalizationLocalization
-import Mathbin.RingTheory.Localization.Submodule
-import Mathbin.RingTheory.DiscreteValuationRing.Tfae
+import RingTheory.Localization.LocalizationLocalization
+import RingTheory.Localization.Submodule
+import RingTheory.DiscreteValuationRing.Tfae
 
 #align_import ring_theory.dedekind_domain.dvr from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 
@@ -55,7 +55,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 open scoped nonZeroDivisors Polynomial
 
 #print IsDedekindDomainDvr /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.dvr
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Localization.LocalizationLocalization
 import Mathbin.RingTheory.Localization.Submodule
 import Mathbin.RingTheory.DiscreteValuationRing.Tfae
 
+#align_import ring_theory.dedekind_domain.dvr from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # Dedekind domains
 
@@ -58,7 +55,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 open scoped nonZeroDivisors Polynomial
 
 #print IsDedekindDomainDvr /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
 

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

@@ -72,6 +72,7 @@ structure IsDedekindDomainDvr : Prop where
 #align is_dedekind_domain_dvr IsDedekindDomainDvr
 -/
 
+#print Ring.DimensionLEOne.localization /-
 /-- Localizing a domain of Krull dimension `≤ 1` gives another ring of Krull dimension `≤ 1`.
 
 Note that the same proof can/should be generalized to preserving any Krull dimension,
@@ -93,7 +94,9 @@ theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing
   refine' h.not_lt_lt ⊥ (Ideal.comap _ _) (Ideal.comap _ _) ⟨_, hpP'⟩
   exact IsLocalization.bot_lt_comap_prime _ _ hM _ hp0
 #align ring.dimension_le_one.localization Ring.DimensionLEOne.localization
+-/
 
+#print IsLocalization.isDedekindDomain /-
 /-- The localization of a Dedekind domain is a Dedekind domain. -/
 theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (hM : M ≤ A⁰)
     (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization M Aₘ] :
@@ -118,14 +121,18 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
     rw [hz, SetLike.coe_mk, ← Algebra.smul_def]
     rfl
 #align is_localization.is_dedekind_domain IsLocalization.isDedekindDomain
+-/
 
+#print IsLocalization.AtPrime.isDedekindDomain /-
 /-- The localization of a Dedekind domain at every nonzero prime ideal is a Dedekind domain. -/
 theorem IsLocalization.AtPrime.isDedekindDomain [IsDedekindDomain A] (P : Ideal A) [P.IsPrime]
     (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] :
     IsDedekindDomain Aₘ :=
   IsLocalization.isDedekindDomain A P.primeCompl_le_nonZeroDivisors Aₘ
 #align is_localization.at_prime.is_dedekind_domain IsLocalization.AtPrime.isDedekindDomain
+-/
 
+#print IsLocalization.AtPrime.not_isField /-
 theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _)
     [CommRing Aₘ] [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : ¬IsField Aₘ :=
   by
@@ -141,7 +148,9 @@ theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP :
                 (IsLocalization.injective Aₘ P.prime_compl_le_non_zero_divisors)).mpr
             x_ne)))
 #align is_localization.at_prime.not_is_field IsLocalization.AtPrime.not_isField
+-/
 
+#print IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain /-
 /-- In a Dedekind domain, the localization at every nonzero prime ideal is a DVR. -/
 theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedekindDomain A]
     {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ]
@@ -155,6 +164,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
     ((DiscreteValuationRing.TFAE Aₘ hnf).out 0 2).mpr
       (IsLocalization.AtPrime.isDedekindDomain A P _)
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
+-/
 
 #print IsDedekindDomain.isDedekindDomainDvr /-
 /-- Dedekind domains, in the sense of Noetherian integrally closed domains of Krull dimension ≤ 1,

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
 
 ! This file was ported from Lean 3 source module ring_theory.dedekind_domain.dvr
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.DiscreteValuationRing.Tfae
 /-!
 # Dedekind domains
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines an equivalent notion of a Dedekind domain (or Dedekind ring),
 namely a Noetherian integral domain where the localization at all nonzero prime ideals is a DVR
 (TODO: and shows that implies the main definition).

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

@@ -55,7 +55,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 open scoped nonZeroDivisors Polynomial
 
 #print IsDedekindDomainDvr /-
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
 

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

@@ -54,6 +54,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 
 open scoped nonZeroDivisors Polynomial
 
+#print IsDedekindDomainDvr /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
@@ -66,6 +67,7 @@ structure IsDedekindDomainDvr : Prop where
   is_dvr_at_nonzero_prime :
     ∀ (P) (_ : P ≠ (⊥ : Ideal A)), P.IsPrime → DiscreteValuationRing (Localization.AtPrime P)
 #align is_dedekind_domain_dvr IsDedekindDomainDvr
+-/
 
 /-- Localizing a domain of Krull dimension `≤ 1` gives another ring of Krull dimension `≤ 1`.
 
@@ -151,6 +153,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
       (IsLocalization.AtPrime.isDedekindDomain A P _)
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
 
+#print IsDedekindDomain.isDedekindDomainDvr /-
 /-- Dedekind domains, in the sense of Noetherian integrally closed domains of Krull dimension ≤ 1,
 are also Dedekind domains in the sense of Noetherian domains where the localization at every
 nonzero prime ideal is a DVR. -/
@@ -159,4 +162,5 @@ theorem IsDedekindDomain.isDedekindDomainDvr [IsDedekindDomain A] : IsDedekindDo
     is_dvr_at_nonzero_prime := fun P hP pP =>
       IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain A hP _ }
 #align is_dedekind_domain.is_dedekind_domain_dvr IsDedekindDomain.isDedekindDomainDvr
+-/
 

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

@@ -147,7 +147,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
   letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
   have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
   exact
-    ((DiscreteValuationRing.tFAE Aₘ hnf).out 0 2).mpr
+    ((DiscreteValuationRing.TFAE Aₘ hnf).out 0 2).mpr
       (IsLocalization.AtPrime.isDedekindDomain A P _)
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
 

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

@@ -72,9 +72,9 @@ structure IsDedekindDomainDvr : Prop where
 Note that the same proof can/should be generalized to preserving any Krull dimension,
 once we have a suitable definition.
 -/
-theorem Ring.DimensionLeOne.localization {R : Type _} (Rₘ : Type _) [CommRing R] [IsDomain R]
+theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing R] [IsDomain R]
     [CommRing Rₘ] [Algebra R Rₘ] {M : Submonoid R} [IsLocalization M Rₘ] (hM : M ≤ R⁰)
-    (h : Ring.DimensionLeOne R) : Ring.DimensionLeOne Rₘ :=
+    (h : Ring.DimensionLEOne R) : Ring.DimensionLEOne Rₘ :=
   by
   intro p hp0 hpp
   refine' ideal.is_maximal_def.mpr ⟨hpp.ne_top, Ideal.maximal_of_no_maximal fun P hpP hPm => _⟩
@@ -87,7 +87,7 @@ theorem Ring.DimensionLeOne.localization {R : Type _} (Rₘ : Type _) [CommRing
   have hlt : Ideal.comap (algebraMap R Rₘ) p < Ideal.comap (algebraMap R Rₘ) P := hpP'
   refine' h.not_lt_lt ⊥ (Ideal.comap _ _) (Ideal.comap _ _) ⟨_, hpP'⟩
   exact IsLocalization.bot_lt_comap_prime _ _ hM _ hp0
-#align ring.dimension_le_one.localization Ring.DimensionLeOne.localization
+#align ring.dimension_le_one.localization Ring.DimensionLEOne.localization
 
 /-- The localization of a Dedekind domain is a Dedekind domain. -/
 theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (hM : M ≤ A⁰)
@@ -142,13 +142,13 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
     {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ]
     [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
   classical
-    letI : IsNoetherianRing Aₘ :=
-      IsLocalization.isNoetherianRing P.prime_compl _ IsDedekindDomain.isNoetherianRing
-    letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
-    have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
-    exact
-      ((DiscreteValuationRing.tFAE Aₘ hnf).out 0 2).mpr
-        (IsLocalization.AtPrime.isDedekindDomain A P _)
+  letI : IsNoetherianRing Aₘ :=
+    IsLocalization.isNoetherianRing P.prime_compl _ IsDedekindDomain.isNoetherianRing
+  letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
+  have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
+  exact
+    ((DiscreteValuationRing.tFAE Aₘ hnf).out 0 2).mpr
+      (IsLocalization.AtPrime.isDedekindDomain A P _)
 #align is_localization.at_prime.discrete_valuation_ring_of_dedekind_domain IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain
 
 /-- Dedekind domains, in the sense of Noetherian integrally closed domains of Krull dimension ≤ 1,

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

@@ -79,7 +79,7 @@ theorem Ring.DimensionLeOne.localization {R : Type _} (Rₘ : Type _) [CommRing
   intro p hp0 hpp
   refine' ideal.is_maximal_def.mpr ⟨hpp.ne_top, Ideal.maximal_of_no_maximal fun P hpP hPm => _⟩
   have hpP' : (⟨p, hpp⟩ : { p : Ideal Rₘ // p.IsPrime }) < ⟨P, hPm.is_prime⟩ := hpP
-  rw [← (IsLocalization.orderIsoOfPrime M Rₘ).lt_iff_lt] at hpP'
+  rw [← (IsLocalization.orderIsoOfPrime M Rₘ).lt_iff_lt] at hpP' 
   haveI : Ideal.IsPrime (Ideal.comap (algebraMap R Rₘ) p) :=
     ((IsLocalization.orderIsoOfPrime M Rₘ) ⟨p, hpp⟩).2.1
   haveI : Ideal.IsPrime (Ideal.comap (algebraMap R Rₘ) P) :=

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

@@ -110,7 +110,7 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
     obtain ⟨⟨y, y_mem⟩, hy⟩ := hx.exists_multiple_integral_of_is_localization M _
     obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindDomain.isIntegrallyClosed hy
     refine' ⟨IsLocalization.mk' Aₘ z ⟨y, y_mem⟩, (IsLocalization.lift_mk'_spec _ _ _ _).mpr _⟩
-    rw [hz, [anonymous], ← Algebra.smul_def]
+    rw [hz, SetLike.coe_mk, ← Algebra.smul_def]
     rfl
 #align is_localization.is_dedekind_domain IsLocalization.isDedekindDomain
 

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

@@ -52,7 +52,7 @@ dedekind domain, dedekind ring
 
 variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 
-open nonZeroDivisors Polynomial
+open scoped nonZeroDivisors Polynomial
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the

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

@@ -4,14 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
 
 ! This file was ported from Lean 3 source module ring_theory.dedekind_domain.dvr
-! leanprover-community/mathlib commit c163ec99dfc664628ca15d215fce0a5b9c265b68
+! 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.DedekindDomain.Ideal
-import Mathbin.RingTheory.DiscreteValuationRing.Tfae
-import Mathbin.RingTheory.Localization.AtPrime
+import Mathbin.RingTheory.Localization.LocalizationLocalization
 import Mathbin.RingTheory.Localization.Submodule
+import Mathbin.RingTheory.DiscreteValuationRing.Tfae
 
 /-!
 # Dedekind domains

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -4,15 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
 
 ! This file was ported from Lean 3 source module ring_theory.dedekind_domain.dvr
-! leanprover-community/mathlib commit 926daa81fd8acb2a04e15572c4ff20af2753c2ae
+! leanprover-community/mathlib commit c163ec99dfc664628ca15d215fce0a5b9c265b68
 ! 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.DiscreteValuationRing
+import Mathbin.RingTheory.DiscreteValuationRing.Tfae
 import Mathbin.RingTheory.Localization.AtPrime
 import Mathbin.RingTheory.Localization.Submodule
-import Mathbin.RingTheory.Valuation.Tfae
 
 /-!
 # Dedekind domains

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

@@ -56,7 +56,7 @@ variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 
 open nonZeroDivisors Polynomial
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (P «expr ≠ » («expr⊥»() : ideal[ideal] A)) -/
 /-- A Dedekind domain is an integral domain that is Noetherian, and the
 localization at every nonzero prime is a discrete valuation ring.
 

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

This refactor adds a new definition IsIntegrallyClosedIn R A equal to IsIntegralClosure R A A, and redefines IsIntegrallyClosed R to equal IsIntegrallyClosed R (FractionRing A). This should make it possible and convenient to generalize away from the fraction fields.

This also more closely approximates the conventions of the Stacks project.

This is a second attempt at the refactor, after #7116 which was much more messy.

@@ -102,7 +102,7 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
   · exact Ring.DimensionLEOne.localization Aₘ hM
   · intro x hx
     obtain ⟨⟨y, y_mem⟩, hy⟩ := hx.exists_multiple_integral_of_isLocalization M _
-    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindRing.toIsIntegrallyClosed hy
+    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindRing.toIsIntegralClosure hy
     refine' ⟨IsLocalization.mk' Aₘ z ⟨y, y_mem⟩, (IsLocalization.lift_mk'_spec _ _ _ _).mpr _⟩
     rw [hz, ← Algebra.smul_def]
     rfl

@@ -79,8 +79,8 @@ theorem Ring.DimensionLEOne.localization {R : Type*} (Rₘ : Type*) [CommRing R]
     ((IsLocalization.orderIsoOfPrime M Rₘ) ⟨p, hpp⟩).2.1
   haveI : Ideal.IsPrime (Ideal.comap (algebraMap R Rₘ) P) :=
     ((IsLocalization.orderIsoOfPrime M Rₘ) ⟨P, hPm.isPrime⟩).2.1
-  have _ : Ideal.comap (algebraMap R Rₘ) p < Ideal.comap (algebraMap R Rₘ) P := hpP'
-  refine' h.not_lt_lt ⊥ (Ideal.comap _ _) (Ideal.comap _ _) ⟨_, hpP'⟩
+  have hlt : Ideal.comap (algebraMap R Rₘ) p < Ideal.comap (algebraMap R Rₘ) P := hpP'
+  refine' h.not_lt_lt ⊥ (Ideal.comap _ _) (Ideal.comap _ _) ⟨_, hlt⟩
   exact IsLocalization.bot_lt_comap_prime _ _ hM _ hp0⟩
 #align ring.dimension_le_one.localization Ring.DimensionLEOne.localization
 

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -59,8 +59,8 @@ TODO: prove the equivalence.
 -/
 structure IsDedekindDomainDvr : Prop where
   isNoetherianRing : IsNoetherianRing A
-  is_dvr_at_nonzero_prime :
-    ∀ (P) (_ : P ≠ (⊥ : Ideal A)) (_ : P.IsPrime), DiscreteValuationRing (Localization.AtPrime P)
+  is_dvr_at_nonzero_prime : ∀ P ≠ (⊥ : Ideal A), ∀ _ : P.IsPrime,
+    DiscreteValuationRing (Localization.AtPrime P)
 #align is_dedekind_domain_dvr IsDedekindDomainDvr
 
 /-- Localizing a domain of Krull dimension `≤ 1` gives another ring of Krull dimension `≤ 1`.

This PR defines IsDedekindRing as IsDedekindDomain without the bundled IsDomain hypothesis.

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Should.20.60IsDedekindDomain.60.20extend.20.60IsDomain.60.3F

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -102,7 +102,7 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
   · exact Ring.DimensionLEOne.localization Aₘ hM
   · intro x hx
     obtain ⟨⟨y, y_mem⟩, hy⟩ := hx.exists_multiple_integral_of_isLocalization M _
-    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindDomain.toIsIntegrallyClosed hy
+    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindRing.toIsIntegrallyClosed hy
     refine' ⟨IsLocalization.mk' Aₘ z ⟨y, y_mem⟩, (IsLocalization.lift_mk'_spec _ _ _ _).mpr _⟩
     rw [hz, ← Algebra.smul_def]
     rfl
@@ -136,7 +136,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
     [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
   classical
   letI : IsNoetherianRing Aₘ :=
-    IsLocalization.isNoetherianRing P.primeCompl _ IsDedekindDomain.toIsNoetherian
+    IsLocalization.isNoetherianRing P.primeCompl _ IsDedekindRing.toIsNoetherian
   letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
   have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
   exact
@@ -148,7 +148,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
 are also Dedekind domains in the sense of Noetherian domains where the localization at every
 nonzero prime ideal is a DVR. -/
 theorem IsDedekindDomain.isDedekindDomainDvr [IsDedekindDomain A] : IsDedekindDomainDvr A :=
-  { isNoetherianRing := IsDedekindDomain.toIsNoetherian
+  { isNoetherianRing := IsDedekindRing.toIsNoetherian
     is_dvr_at_nonzero_prime := fun _ hP _ =>
       IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain A hP _ }
 #align is_dedekind_domain.is_dedekind_domain_dvr IsDedekindDomain.isDedekindDomainDvr

This redefines the IsDedekindDomain class to be the conjunction through extends of the classes IsDomain, IsNoetherianRing, DimensionLEOne and IsIntegrallyClosed.

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Should.20.60IsDedekindDomain.60.20extend.20.60IsDomain.60.3F

@@ -70,7 +70,7 @@ once we have a suitable definition.
 -/
 theorem Ring.DimensionLEOne.localization {R : Type*} (Rₘ : Type*) [CommRing R] [IsDomain R]
     [CommRing Rₘ] [Algebra R Rₘ] {M : Submonoid R} [IsLocalization M Rₘ] (hM : M ≤ R⁰)
-    (h : Ring.DimensionLEOne R) : Ring.DimensionLEOne Rₘ := ⟨by
+    [h : Ring.DimensionLEOne R] : Ring.DimensionLEOne Rₘ := ⟨by
   intro p hp0 hpp
   refine' Ideal.isMaximal_def.mpr ⟨hpp.ne_top, Ideal.maximal_of_no_maximal fun P hpP hPm => _⟩
   have hpP' : (⟨p, hpp⟩ : { p : Ideal Rₘ // p.IsPrime }) < ⟨P, hPm.isPrime⟩ := hpP
@@ -96,12 +96,13 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
     IsScalarTower.of_algebraMap_eq fun x => (IsLocalization.lift_eq h x).symm
   haveI : IsFractionRing Aₘ (FractionRing A) :=
     IsFractionRing.isFractionRing_of_isDomain_of_isLocalization M _ _
-  refine' (isDedekindDomain_iff _ (FractionRing A)).mpr ⟨_, _, _⟩
+  refine' (isDedekindDomain_iff _ (FractionRing A)).mpr ⟨_, _, _, _⟩
+  · infer_instance
   · exact IsLocalization.isNoetherianRing M _ (by infer_instance)
-  · exact IsDedekindDomain.dimensionLEOne.localization Aₘ hM
+  · exact Ring.DimensionLEOne.localization Aₘ hM
   · intro x hx
     obtain ⟨⟨y, y_mem⟩, hy⟩ := hx.exists_multiple_integral_of_isLocalization M _
-    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindDomain.isIntegrallyClosed hy
+    obtain ⟨z, hz⟩ := (isIntegrallyClosed_iff _).mp IsDedekindDomain.toIsIntegrallyClosed hy
     refine' ⟨IsLocalization.mk' Aₘ z ⟨y, y_mem⟩, (IsLocalization.lift_mk'_spec _ _ _ _).mpr _⟩
     rw [hz, ← Algebra.smul_def]
     rfl
@@ -135,7 +136,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
     [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
   classical
   letI : IsNoetherianRing Aₘ :=
-    IsLocalization.isNoetherianRing P.primeCompl _ IsDedekindDomain.isNoetherianRing
+    IsLocalization.isNoetherianRing P.primeCompl _ IsDedekindDomain.toIsNoetherian
   letI : LocalRing Aₘ := IsLocalization.AtPrime.localRing Aₘ P
   have hnf := IsLocalization.AtPrime.not_isField A hP Aₘ
   exact
@@ -147,7 +148,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
 are also Dedekind domains in the sense of Noetherian domains where the localization at every
 nonzero prime ideal is a DVR. -/
 theorem IsDedekindDomain.isDedekindDomainDvr [IsDedekindDomain A] : IsDedekindDomainDvr A :=
-  { isNoetherianRing := IsDedekindDomain.isNoetherianRing
+  { isNoetherianRing := IsDedekindDomain.toIsNoetherian
     is_dvr_at_nonzero_prime := fun _ hP _ =>
       IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain A hP _ }
 #align is_dedekind_domain.is_dedekind_domain_dvr IsDedekindDomain.isDedekindDomainDvr

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

This has nice performance benefits.

@@ -47,7 +47,7 @@ dedekind domain, dedekind ring
 -/
 
 
-variable (R A K : Type _) [CommRing R] [CommRing A] [IsDomain A] [Field K]
+variable (R A K : Type*) [CommRing R] [CommRing A] [IsDomain A] [Field K]
 
 open scoped nonZeroDivisors Polynomial
 
@@ -68,7 +68,7 @@ structure IsDedekindDomainDvr : Prop where
 Note that the same proof can/should be generalized to preserving any Krull dimension,
 once we have a suitable definition.
 -/
-theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing R] [IsDomain R]
+theorem Ring.DimensionLEOne.localization {R : Type*} (Rₘ : Type*) [CommRing R] [IsDomain R]
     [CommRing Rₘ] [Algebra R Rₘ] {M : Submonoid R} [IsLocalization M Rₘ] (hM : M ≤ R⁰)
     (h : Ring.DimensionLEOne R) : Ring.DimensionLEOne Rₘ := ⟨by
   intro p hp0 hpp
@@ -86,7 +86,7 @@ theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing
 
 /-- The localization of a Dedekind domain is a Dedekind domain. -/
 theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (hM : M ≤ A⁰)
-    (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization M Aₘ] :
+    (Aₘ : Type*) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization M Aₘ] :
     IsDedekindDomain Aₘ := by
   have h : ∀ y : M, IsUnit (algebraMap A (FractionRing A) y) := by
     rintro ⟨y, hy⟩
@@ -109,12 +109,12 @@ theorem IsLocalization.isDedekindDomain [IsDedekindDomain A] {M : Submonoid A} (
 
 /-- The localization of a Dedekind domain at every nonzero prime ideal is a Dedekind domain. -/
 theorem IsLocalization.AtPrime.isDedekindDomain [IsDedekindDomain A] (P : Ideal A) [P.IsPrime]
-    (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] :
+    (Aₘ : Type*) [CommRing Aₘ] [IsDomain Aₘ] [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] :
     IsDedekindDomain Aₘ :=
   IsLocalization.isDedekindDomain A P.primeCompl_le_nonZeroDivisors Aₘ
 #align is_localization.at_prime.is_dedekind_domain IsLocalization.AtPrime.isDedekindDomain
 
-theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _)
+theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type*)
     [CommRing Aₘ] [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : ¬IsField Aₘ := by
   intro h
   letI := h.toField
@@ -131,7 +131,7 @@ theorem IsLocalization.AtPrime.not_isField {P : Ideal A} (hP : P ≠ ⊥) [pP :
 
 /-- In a Dedekind domain, the localization at every nonzero prime ideal is a DVR. -/
 theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedekindDomain A]
-    {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type _) [CommRing Aₘ] [IsDomain Aₘ]
+    {P : Ideal A} (hP : P ≠ ⊥) [pP : P.IsPrime] (Aₘ : Type*) [CommRing Aₘ] [IsDomain Aₘ]
     [Algebra A Aₘ] [IsLocalization.AtPrime Aₘ P] : DiscreteValuationRing Aₘ := by
   classical
   letI : IsNoetherianRing Aₘ :=

The predicate that a ring has Krull dimension at most one was a regular def. I believe we should turn it into a class because:

• The property follows from the ring structure, e.g. because it is a PID or because it is an integral closure.
• We pass it around as a whole hypothesis, something instance synthesis can deal well with.
• It makes the definition of IsDedekindDomain the conjunction of a number of classes, so we could switch to extends for all its fields.

The main change in API is the addition of Ideal.IsPrime.isMaximal which is a restatement of the Krull dimension property with convenient dot notation: turn a prime ideal into a maximal ideal given the hypothesis that it's not zero.

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Should.20.60IsDedekindDomain.60.20extend.20.60IsDomain.60.3F/near/374515392

@@ -70,7 +70,7 @@ once we have a suitable definition.
 -/
 theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing R] [IsDomain R]
     [CommRing Rₘ] [Algebra R Rₘ] {M : Submonoid R} [IsLocalization M Rₘ] (hM : M ≤ R⁰)
-    (h : Ring.DimensionLEOne R) : Ring.DimensionLEOne Rₘ := by
+    (h : Ring.DimensionLEOne R) : Ring.DimensionLEOne Rₘ := ⟨by
   intro p hp0 hpp
   refine' Ideal.isMaximal_def.mpr ⟨hpp.ne_top, Ideal.maximal_of_no_maximal fun P hpP hPm => _⟩
   have hpP' : (⟨p, hpp⟩ : { p : Ideal Rₘ // p.IsPrime }) < ⟨P, hPm.isPrime⟩ := hpP
@@ -81,7 +81,7 @@ theorem Ring.DimensionLEOne.localization {R : Type _} (Rₘ : Type _) [CommRing
     ((IsLocalization.orderIsoOfPrime M Rₘ) ⟨P, hPm.isPrime⟩).2.1
   have _ : Ideal.comap (algebraMap R Rₘ) p < Ideal.comap (algebraMap R Rₘ) P := hpP'
   refine' h.not_lt_lt ⊥ (Ideal.comap _ _) (Ideal.comap _ _) ⟨_, hpP'⟩
-  exact IsLocalization.bot_lt_comap_prime _ _ hM _ hp0
+  exact IsLocalization.bot_lt_comap_prime _ _ hM _ hp0⟩
 #align ring.dimension_le_one.localization Ring.DimensionLEOne.localization
 
 /-- The localization of a Dedekind domain is a Dedekind domain. -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.dvr
-! 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.Localization.LocalizationLocalization
 import Mathlib.RingTheory.Localization.Submodule
 import Mathlib.RingTheory.DiscreteValuationRing.TFAE
 
+#align_import ring_theory.dedekind_domain.dvr from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Dedekind domains
 

@@ -61,7 +61,7 @@ This is equivalent to `IsDedekindDomain`.
 TODO: prove the equivalence.
 -/
 structure IsDedekindDomainDvr : Prop where
-  IsNoetherianRing : IsNoetherianRing A
+  isNoetherianRing : IsNoetherianRing A
   is_dvr_at_nonzero_prime :
     ∀ (P) (_ : P ≠ (⊥ : Ideal A)) (_ : P.IsPrime), DiscreteValuationRing (Localization.AtPrime P)
 #align is_dedekind_domain_dvr IsDedekindDomainDvr
@@ -150,7 +150,7 @@ theorem IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain [IsDedek
 are also Dedekind domains in the sense of Noetherian domains where the localization at every
 nonzero prime ideal is a DVR. -/
 theorem IsDedekindDomain.isDedekindDomainDvr [IsDedekindDomain A] : IsDedekindDomainDvr A :=
-  { IsNoetherianRing := IsDedekindDomain.isNoetherianRing
+  { isNoetherianRing := IsDedekindDomain.isNoetherianRing
     is_dvr_at_nonzero_prime := fun _ hP _ =>
       IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain A hP _ }
 #align is_dedekind_domain.is_dedekind_domain_dvr IsDedekindDomain.isDedekindDomainDvr

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