ring_theory.dedekind_domain.finite_adele_ring ⟷ Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing

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

@@ -182,9 +182,9 @@ theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
-    rw [mem_set_of_eq] at hv 
+    rw [mem_set_of_eq] at hv
     contrapose! hv
-    rw [mem_adic_completion_integers, mem_adic_completion_integers, ← max_le_iff] at hv 
+    rw [mem_adic_completion_integers, mem_adic_completion_integers, ← max_le_iff] at hv
     rw [mem_adic_completion_integers, Pi.add_apply]
     exact le_trans (valued.v.map_add_le_max' (x v) (y v)) hv
   exact (hx.union hy).Subset h_subset
@@ -200,7 +200,7 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
     {v : height_one_spectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
+    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
     have h_zero : (Valued.v (0 : v.adic_completion K) : WithZero (Multiplicative ℤ)) = 0 :=
       valued.v.map_zero'
     rw [h_zero]; exact zero_le_one' _
@@ -237,9 +237,9 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
-    rw [mem_set_of_eq] at hv 
+    rw [mem_set_of_eq] at hv
     contrapose! hv
-    rw [mem_adic_completion_integers, mem_adic_completion_integers] at hv 
+    rw [mem_adic_completion_integers, mem_adic_completion_integers] at hv
     have h_mul : Valued.v (x v * y v) = Valued.v (x v) * Valued.v (y v) :=
       Valued.v.map_mul' (x v) (y v)
     rw [mem_adic_completion_integers, Pi.mul_apply, h_mul]
@@ -259,7 +259,7 @@ theorem one : (1 : K_hat R K).IsFiniteAdele :=
     {v : height_one_spectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
+    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
     exact le_of_eq valued.v.map_one'
   simp_rw [Pi.one_apply, h_empty]
   exact finite_empty

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

@@ -244,8 +244,8 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
       Valued.v.map_mul' (x v) (y v)
     rw [mem_adic_completion_integers, Pi.mul_apply, h_mul]
     exact
-      @mul_le_one' (WithZero (Multiplicative ℤ)) _ _ (OrderedCommMonoid.to_covariantClass_left _) _
-        _ hv.left hv.right
+      @mul_le_one' (WithZero (Multiplicative ℤ)) _ _ (OrderedCommMonoid.toCovariantClassLeft _) _ _
+        hv.left hv.right
   exact (hx.union hy).Subset h_subset
 #align dedekind_domain.prod_adic_completions.is_finite_adele.mul DedekindDomain.ProdAdicCompletions.IsFiniteAdele.mul
 -/

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

@@ -3,7 +3,7 @@ Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: María Inés de Frutos-Fernández
 -/
-import Mathbin.RingTheory.DedekindDomain.AdicValuation
+import RingTheory.DedekindDomain.AdicValuation
 
 #align_import ring_theory.dedekind_domain.finite_adele_ring from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -280,7 +280,7 @@ of `adic_completion` with respect to `adic_completion_integers`. -/
 noncomputable def finiteAdeleRing : Subring (K_hat R K)
     where
   carrier := {x : K_hat R K | x.IsFiniteAdele}
-  mul_mem' _ _ hx hy := mul hx hy
+  hMul_mem' _ _ hx hy := mul hx hy
   one_mem' := one
   add_mem' _ _ hx hy := add hx hy
   zero_mem' := zero

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

@@ -2,14 +2,11 @@
 Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: María Inés de Frutos-Fernández
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.finite_adele_ring
-! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.DedekindDomain.AdicValuation
 
+#align_import ring_theory.dedekind_domain.finite_adele_ring from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
+
 /-!
 # The finite adèle ring of a Dedekind domain
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: María Inés de Frutos-Fernández
 
 ! This file was ported from Lean 3 source module ring_theory.dedekind_domain.finite_adele_ring
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.RingTheory.DedekindDomain.AdicValuation
 
 /-!
 # The finite adèle ring of a Dedekind domain
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 We define the ring of finite adèles of a Dedekind domain `R`.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -43,19 +43,23 @@ namespace DedekindDomain
 variable (R K : Type _) [CommRing R] [IsDomain R] [IsDedekindDomain R] [Field K] [Algebra R K]
   [IsFractionRing R K] (v : HeightOneSpectrum R)
 
+#print DedekindDomain.FiniteIntegralAdeles /-
 /-- The product of all `adic_completion_integers`, where `v` runs over the maximal ideals of `R`. -/
 def FiniteIntegralAdeles : Type _ :=
   ∀ v : HeightOneSpectrum R, v.adicCompletionIntegers K
 deriving CommRing, TopologicalSpace, Inhabited
 #align dedekind_domain.finite_integral_adeles DedekindDomain.FiniteIntegralAdeles
+-/
 
 local notation "R_hat" => FiniteIntegralAdeles
 
+#print DedekindDomain.ProdAdicCompletions /-
 /-- The product of all `adic_completion`, where `v` runs over the maximal ideals of `R`. -/
 def ProdAdicCompletions :=
   ∀ v : HeightOneSpectrum R, v.adicCompletion K
 deriving NonUnitalNonAssocRing, TopologicalSpace, TopologicalRing, CommRing, Inhabited
 #align dedekind_domain.prod_adic_completions DedekindDomain.ProdAdicCompletions
+-/
 
 local notation "K_hat" => ProdAdicCompletions
 
@@ -63,10 +67,13 @@ namespace FiniteIntegralAdeles
 
 noncomputable instance : Coe (R_hat R K) (K_hat R K) where coe x v := x v
 
+#print DedekindDomain.FiniteIntegralAdeles.coe_apply /-
 theorem coe_apply (x : R_hat R K) (v : HeightOneSpectrum R) : (x : K_hat R K) v = ↑(x v) :=
   rfl
 #align dedekind_domain.finite_integral_adeles.coe_apply DedekindDomain.FiniteIntegralAdeles.coe_apply
+-/
 
+#print DedekindDomain.FiniteIntegralAdeles.Coe.addMonoidHom /-
 /-- The inclusion of `R_hat` in `K_hat` as a homomorphism of additive monoids. -/
 @[simps]
 def Coe.addMonoidHom : AddMonoidHom (R_hat R K) (K_hat R K)
@@ -75,7 +82,9 @@ def Coe.addMonoidHom : AddMonoidHom (R_hat R K) (K_hat R K)
   map_zero' := rfl
   map_add' x y := by ext v; simp only [coe_apply, Pi.add_apply, Subring.coe_add]
 #align dedekind_domain.finite_integral_adeles.coe.add_monoid_hom DedekindDomain.FiniteIntegralAdeles.Coe.addMonoidHom
+-/
 
+#print DedekindDomain.FiniteIntegralAdeles.Coe.ringHom /-
 /-- The inclusion of `R_hat` in `K_hat` as a ring homomorphism. -/
 @[simps]
 def Coe.ringHom : RingHom (R_hat R K) (K_hat R K) :=
@@ -84,6 +93,7 @@ def Coe.ringHom : RingHom (R_hat R K) (K_hat R K) :=
     map_one' := rfl
     map_mul' := fun x y => by ext p; simp only [Pi.mul_apply, Subring.coe_mul]; rfl }
 #align dedekind_domain.finite_integral_adeles.coe.ring_hom DedekindDomain.FiniteIntegralAdeles.Coe.ringHom
+-/
 
 end FiniteIntegralAdeles
 
@@ -92,9 +102,11 @@ section AlgebraInstances
 instance : Algebra K (K_hat R K) :=
   (by infer_instance : Algebra K <| ∀ v : HeightOneSpectrum R, v.adicCompletion K)
 
+#print DedekindDomain.ProdAdicCompletions.algebra' /-
 instance ProdAdicCompletions.algebra' : Algebra R (K_hat R K) :=
   (by infer_instance : Algebra R <| ∀ v : HeightOneSpectrum R, v.adicCompletion K)
 #align dedekind_domain.prod_adic_completions.algebra' DedekindDomain.ProdAdicCompletions.algebra'
+-/
 
 instance : IsScalarTower R K (K_hat R K) :=
   (by infer_instance : IsScalarTower R K <| ∀ v : HeightOneSpectrum R, v.adicCompletion K)
@@ -102,30 +114,38 @@ instance : IsScalarTower R K (K_hat R K) :=
 instance : Algebra R (R_hat R K) :=
   (by infer_instance : Algebra R <| ∀ v : HeightOneSpectrum R, v.adicCompletionIntegers K)
 
+#print DedekindDomain.ProdAdicCompletions.algebraCompletions /-
 instance ProdAdicCompletions.algebraCompletions : Algebra (R_hat R K) (K_hat R K) :=
   (FiniteIntegralAdeles.Coe.ringHom R K).toAlgebra
 #align dedekind_domain.prod_adic_completions.algebra_completions DedekindDomain.ProdAdicCompletions.algebraCompletions
+-/
 
+#print DedekindDomain.ProdAdicCompletions.isScalarTower_completions /-
 instance ProdAdicCompletions.isScalarTower_completions : IsScalarTower R (R_hat R K) (K_hat R K) :=
   (by infer_instance :
     IsScalarTower R (∀ v : HeightOneSpectrum R, v.adicCompletionIntegers K) <|
       ∀ v : HeightOneSpectrum R, v.adicCompletion K)
 #align dedekind_domain.prod_adic_completions.is_scalar_tower_completions DedekindDomain.ProdAdicCompletions.isScalarTower_completions
+-/
 
 end AlgebraInstances
 
 namespace FiniteIntegralAdeles
 
+#print DedekindDomain.FiniteIntegralAdeles.Coe.algHom /-
 /-- The inclusion of `R_hat` in `K_hat` as an algebra homomorphism. -/
 def Coe.algHom : AlgHom R (R_hat R K) (K_hat R K) :=
   { Coe.ringHom R K with
     toFun := coe
     commutes' := fun r => rfl }
 #align dedekind_domain.finite_integral_adeles.coe.alg_hom DedekindDomain.FiniteIntegralAdeles.Coe.algHom
+-/
 
+#print DedekindDomain.FiniteIntegralAdeles.Coe.algHom_apply /-
 theorem Coe.algHom_apply (x : R_hat R K) (v : HeightOneSpectrum R) : (Coe.algHom R K) x v = x v :=
   rfl
 #align dedekind_domain.finite_integral_adeles.coe.alg_hom_apply DedekindDomain.FiniteIntegralAdeles.Coe.algHom_apply
+-/
 
 end FiniteIntegralAdeles
 
@@ -139,14 +159,17 @@ namespace ProdAdicCompletions
 
 variable {R K}
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele /-
 /-- An element `x : K_hat R K` is a finite adèle if for all but finitely many height one ideals
   `v`, the component `x v` is a `v`-adic integer. -/
 def IsFiniteAdele (x : K_hat R K) :=
   ∀ᶠ v : HeightOneSpectrum R in Filter.cofinite, x v ∈ v.adicCompletionIntegers K
 #align dedekind_domain.prod_adic_completions.is_finite_adele DedekindDomain.ProdAdicCompletions.IsFiniteAdele
+-/
 
 namespace IsFiniteAdele
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele.add /-
 /-- The sum of two finite adèles is a finite adèle. -/
 theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     (x + y).IsFiniteAdele :=
@@ -166,7 +189,9 @@ theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     exact le_trans (valued.v.map_add_le_max' (x v) (y v)) hv
   exact (hx.union hy).Subset h_subset
 #align dedekind_domain.prod_adic_completions.is_finite_adele.add DedekindDomain.ProdAdicCompletions.IsFiniteAdele.add
+-/
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele.zero /-
 /-- The tuple `(0)_v` is a finite adèle. -/
 theorem zero : (0 : K_hat R K).IsFiniteAdele :=
   by
@@ -182,7 +207,9 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
   simp_rw [Pi.zero_apply, h_empty]
   exact finite_empty
 #align dedekind_domain.prod_adic_completions.is_finite_adele.zero DedekindDomain.ProdAdicCompletions.IsFiniteAdele.zero
+-/
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele.neg /-
 /-- The negative of a finite adèle is a finite adèle. -/
 theorem neg {x : K_hat R K} (hx : x.IsFiniteAdele) : (-x).IsFiniteAdele :=
   by
@@ -195,7 +222,9 @@ theorem neg {x : K_hat R K} (hx : x.IsFiniteAdele) : (-x).IsFiniteAdele :=
     rw [mem_adic_completion_integers, mem_adic_completion_integers, Valuation.map_neg]
   simpa only [Pi.neg_apply, h] using hx
 #align dedekind_domain.prod_adic_completions.is_finite_adele.neg DedekindDomain.ProdAdicCompletions.IsFiniteAdele.neg
+-/
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele.mul /-
 /-- The product of two finite adèles is a finite adèle. -/
 theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     (x * y).IsFiniteAdele :=
@@ -219,7 +248,9 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
         _ hv.left hv.right
   exact (hx.union hy).Subset h_subset
 #align dedekind_domain.prod_adic_completions.is_finite_adele.mul DedekindDomain.ProdAdicCompletions.IsFiniteAdele.mul
+-/
 
+#print DedekindDomain.ProdAdicCompletions.IsFiniteAdele.one /-
 /-- The tuple `(1)_v` is a finite adèle. -/
 theorem one : (1 : K_hat R K).IsFiniteAdele :=
   by
@@ -233,6 +264,7 @@ theorem one : (1 : K_hat R K).IsFiniteAdele :=
   simp_rw [Pi.one_apply, h_empty]
   exact finite_empty
 #align dedekind_domain.prod_adic_completions.is_finite_adele.one DedekindDomain.ProdAdicCompletions.IsFiniteAdele.one
+-/
 
 end IsFiniteAdele
 
@@ -242,6 +274,7 @@ open ProdAdicCompletions.IsFiniteAdele
 
 variable (R K)
 
+#print DedekindDomain.finiteAdeleRing /-
 /-- The finite adèle ring of `R` is the restricted product over all maximal ideals `v` of `R`
 of `adic_completion` with respect to `adic_completion_integers`. -/
 noncomputable def finiteAdeleRing : Subring (K_hat R K)
@@ -253,13 +286,16 @@ noncomputable def finiteAdeleRing : Subring (K_hat R K)
   zero_mem' := zero
   neg_mem' _ hx := neg hx
 #align dedekind_domain.finite_adele_ring DedekindDomain.finiteAdeleRing
+-/
 
 variable {R K}
 
+#print DedekindDomain.mem_finiteAdeleRing_iff /-
 @[simp]
 theorem mem_finiteAdeleRing_iff (x : K_hat R K) : x ∈ finiteAdeleRing R K ↔ x.IsFiniteAdele :=
   Iff.rfl
 #align dedekind_domain.mem_finite_adele_ring_iff DedekindDomain.mem_finiteAdeleRing_iff
+-/
 
 end DedekindDomain
 

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

@@ -49,7 +49,6 @@ def FiniteIntegralAdeles : Type _ :=
 deriving CommRing, TopologicalSpace, Inhabited
 #align dedekind_domain.finite_integral_adeles DedekindDomain.FiniteIntegralAdeles
 
--- mathport name: exprR_hat
 local notation "R_hat" => FiniteIntegralAdeles
 
 /-- The product of all `adic_completion`, where `v` runs over the maximal ideals of `R`. -/
@@ -58,7 +57,6 @@ def ProdAdicCompletions :=
 deriving NonUnitalNonAssocRing, TopologicalSpace, TopologicalRing, CommRing, Inhabited
 #align dedekind_domain.prod_adic_completions DedekindDomain.ProdAdicCompletions
 
--- mathport name: exprK_hat
 local notation "K_hat" => ProdAdicCompletions
 
 namespace FiniteIntegralAdeles

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

@@ -155,9 +155,9 @@ theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
   by
   rw [is_finite_adele, Filter.eventually_cofinite] at hx hy ⊢
   have h_subset :
-    { v : height_one_spectrum R | ¬(x + y) v ∈ v.adicCompletionIntegers K } ⊆
-      { v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K } ∪
-        { v : height_one_spectrum R | ¬y v ∈ v.adicCompletionIntegers K } :=
+    {v : height_one_spectrum R | ¬(x + y) v ∈ v.adicCompletionIntegers K} ⊆
+      {v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K} ∪
+        {v : height_one_spectrum R | ¬y v ∈ v.adicCompletionIntegers K} :=
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
@@ -174,7 +174,7 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
   by
   rw [is_finite_adele, Filter.eventually_cofinite]
   have h_empty :
-    { v : height_one_spectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
+    {v : height_one_spectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
     rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
@@ -204,9 +204,9 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
   by
   rw [is_finite_adele, Filter.eventually_cofinite] at hx hy ⊢
   have h_subset :
-    { v : height_one_spectrum R | ¬(x * y) v ∈ v.adicCompletionIntegers K } ⊆
-      { v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K } ∪
-        { v : height_one_spectrum R | ¬y v ∈ v.adicCompletionIntegers K } :=
+    {v : height_one_spectrum R | ¬(x * y) v ∈ v.adicCompletionIntegers K} ⊆
+      {v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K} ∪
+        {v : height_one_spectrum R | ¬y v ∈ v.adicCompletionIntegers K} :=
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
@@ -227,7 +227,7 @@ theorem one : (1 : K_hat R K).IsFiniteAdele :=
   by
   rw [is_finite_adele, Filter.eventually_cofinite]
   have h_empty :
-    { v : height_one_spectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
+    {v : height_one_spectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
     rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
@@ -248,7 +248,7 @@ variable (R K)
 of `adic_completion` with respect to `adic_completion_integers`. -/
 noncomputable def finiteAdeleRing : Subring (K_hat R K)
     where
-  carrier := { x : K_hat R K | x.IsFiniteAdele }
+  carrier := {x : K_hat R K | x.IsFiniteAdele}
   mul_mem' _ _ hx hy := mul hx hy
   one_mem' := one
   add_mem' _ _ hx hy := add hx hy

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

@@ -45,8 +45,8 @@ variable (R K : Type _) [CommRing R] [IsDomain R] [IsDedekindDomain R] [Field K]
 
 /-- The product of all `adic_completion_integers`, where `v` runs over the maximal ideals of `R`. -/
 def FiniteIntegralAdeles : Type _ :=
-  ∀ v : HeightOneSpectrum R, v.adicCompletionIntegers K deriving CommRing, TopologicalSpace,
-  Inhabited
+  ∀ v : HeightOneSpectrum R, v.adicCompletionIntegers K
+deriving CommRing, TopologicalSpace, Inhabited
 #align dedekind_domain.finite_integral_adeles DedekindDomain.FiniteIntegralAdeles
 
 -- mathport name: exprR_hat
@@ -54,8 +54,8 @@ local notation "R_hat" => FiniteIntegralAdeles
 
 /-- The product of all `adic_completion`, where `v` runs over the maximal ideals of `R`. -/
 def ProdAdicCompletions :=
-  ∀ v : HeightOneSpectrum R, v.adicCompletion K deriving NonUnitalNonAssocRing, TopologicalSpace,
-  TopologicalRing, CommRing, Inhabited
+  ∀ v : HeightOneSpectrum R, v.adicCompletion K
+deriving NonUnitalNonAssocRing, TopologicalSpace, TopologicalRing, CommRing, Inhabited
 #align dedekind_domain.prod_adic_completions DedekindDomain.ProdAdicCompletions
 
 -- mathport name: exprK_hat
@@ -153,7 +153,7 @@ namespace IsFiniteAdele
 theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     (x + y).IsFiniteAdele :=
   by
-  rw [is_finite_adele, Filter.eventually_cofinite] at hx hy⊢
+  rw [is_finite_adele, Filter.eventually_cofinite] at hx hy ⊢
   have h_subset :
     { v : height_one_spectrum R | ¬(x + y) v ∈ v.adicCompletionIntegers K } ⊆
       { v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K } ∪
@@ -161,9 +161,9 @@ theorem add {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
-    rw [mem_set_of_eq] at hv
+    rw [mem_set_of_eq] at hv 
     contrapose! hv
-    rw [mem_adic_completion_integers, mem_adic_completion_integers, ← max_le_iff] at hv
+    rw [mem_adic_completion_integers, mem_adic_completion_integers, ← max_le_iff] at hv 
     rw [mem_adic_completion_integers, Pi.add_apply]
     exact le_trans (valued.v.map_add_le_max' (x v) (y v)) hv
   exact (hx.union hy).Subset h_subset
@@ -177,7 +177,7 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
     { v : height_one_spectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
+    rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
     have h_zero : (Valued.v (0 : v.adic_completion K) : WithZero (Multiplicative ℤ)) = 0 :=
       valued.v.map_zero'
     rw [h_zero]; exact zero_le_one' _
@@ -188,7 +188,7 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
 /-- The negative of a finite adèle is a finite adèle. -/
 theorem neg {x : K_hat R K} (hx : x.IsFiniteAdele) : (-x).IsFiniteAdele :=
   by
-  rw [is_finite_adele] at hx⊢
+  rw [is_finite_adele] at hx ⊢
   have h :
     ∀ v : height_one_spectrum R,
       -x v ∈ v.adicCompletionIntegers K ↔ x v ∈ v.adicCompletionIntegers K :=
@@ -202,7 +202,7 @@ theorem neg {x : K_hat R K} (hx : x.IsFiniteAdele) : (-x).IsFiniteAdele :=
 theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     (x * y).IsFiniteAdele :=
   by
-  rw [is_finite_adele, Filter.eventually_cofinite] at hx hy⊢
+  rw [is_finite_adele, Filter.eventually_cofinite] at hx hy ⊢
   have h_subset :
     { v : height_one_spectrum R | ¬(x * y) v ∈ v.adicCompletionIntegers K } ⊆
       { v : height_one_spectrum R | ¬x v ∈ v.adicCompletionIntegers K } ∪
@@ -210,9 +210,9 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     by
     intro v hv
     rw [mem_union, mem_set_of_eq, mem_set_of_eq]
-    rw [mem_set_of_eq] at hv
+    rw [mem_set_of_eq] at hv 
     contrapose! hv
-    rw [mem_adic_completion_integers, mem_adic_completion_integers] at hv
+    rw [mem_adic_completion_integers, mem_adic_completion_integers] at hv 
     have h_mul : Valued.v (x v * y v) = Valued.v (x v) * Valued.v (y v) :=
       Valued.v.map_mul' (x v) (y v)
     rw [mem_adic_completion_integers, Pi.mul_apply, h_mul]
@@ -230,7 +230,7 @@ theorem one : (1 : K_hat R K).IsFiniteAdele :=
     { v : height_one_spectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
     by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
+    rw [mem_set_of_eq] at hv ; apply hv; rw [mem_adic_completion_integers]
     exact le_of_eq valued.v.map_one'
   simp_rw [Pi.one_apply, h_empty]
   exact finite_empty

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

@@ -75,9 +75,7 @@ def Coe.addMonoidHom : AddMonoidHom (R_hat R K) (K_hat R K)
     where
   toFun := coe
   map_zero' := rfl
-  map_add' x y := by
-    ext v
-    simp only [coe_apply, Pi.add_apply, Subring.coe_add]
+  map_add' x y := by ext v; simp only [coe_apply, Pi.add_apply, Subring.coe_add]
 #align dedekind_domain.finite_integral_adeles.coe.add_monoid_hom DedekindDomain.FiniteIntegralAdeles.Coe.addMonoidHom
 
 /-- The inclusion of `R_hat` in `K_hat` as a ring homomorphism. -/
@@ -86,10 +84,7 @@ def Coe.ringHom : RingHom (R_hat R K) (K_hat R K) :=
   { Coe.addMonoidHom R K with
     toFun := coe
     map_one' := rfl
-    map_mul' := fun x y => by
-      ext p
-      simp only [Pi.mul_apply, Subring.coe_mul]
-      rfl }
+    map_mul' := fun x y => by ext p; simp only [Pi.mul_apply, Subring.coe_mul]; rfl }
 #align dedekind_domain.finite_integral_adeles.coe.ring_hom DedekindDomain.FiniteIntegralAdeles.Coe.ringHom
 
 end FiniteIntegralAdeles
@@ -181,16 +176,11 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele :=
   have h_empty :
     { v : height_one_spectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
     by
-    ext v
-    rw [mem_empty_iff_false, iff_false_iff]
-    intro hv
-    rw [mem_set_of_eq] at hv
-    apply hv
-    rw [mem_adic_completion_integers]
+    ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
+    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
     have h_zero : (Valued.v (0 : v.adic_completion K) : WithZero (Multiplicative ℤ)) = 0 :=
       valued.v.map_zero'
-    rw [h_zero]
-    exact zero_le_one' _
+    rw [h_zero]; exact zero_le_one' _
   simp_rw [Pi.zero_apply, h_empty]
   exact finite_empty
 #align dedekind_domain.prod_adic_completions.is_finite_adele.zero DedekindDomain.ProdAdicCompletions.IsFiniteAdele.zero
@@ -239,12 +229,8 @@ theorem one : (1 : K_hat R K).IsFiniteAdele :=
   have h_empty :
     { v : height_one_spectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K } = ∅ :=
     by
-    ext v
-    rw [mem_empty_iff_false, iff_false_iff]
-    intro hv
-    rw [mem_set_of_eq] at hv
-    apply hv
-    rw [mem_adic_completion_integers]
+    ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
+    rw [mem_set_of_eq] at hv; apply hv; rw [mem_adic_completion_integers]
     exact le_of_eq valued.v.map_one'
   simp_rw [Pi.one_apply, h_empty]
   exact finite_empty

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

@@ -4,12 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: María Inés de Frutos-Fernández
 
 ! This file was ported from Lean 3 source module ring_theory.dedekind_domain.finite_adele_ring
-! leanprover-community/mathlib commit a8e7ac804fc39df0340c64906075787e0c90fa60
+! 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.AdicValuation
-import Mathbin.Topology.Algebra.UniformRing
 
 /-!
 # The finite adèle ring of a Dedekind domain

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

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.

@@ -37,7 +37,7 @@ open Function Set IsDedekindDomain IsDedekindDomain.HeightOneSpectrum
 
 namespace DedekindDomain
 
-variable (R K : Type*) [CommRing R] [IsDomain R] [IsDedekindDomain R] [Field K] [Algebra R K]
+variable (R K : Type*) [CommRing R] [IsDedekindDomain R] [Field K] [Algebra R K]
   [IsFractionRing R K] (v : HeightOneSpectrum R)
 
 /-- The product of all `adicCompletionIntegers`, where `v` runs over the maximal ideals of `R`. -/

There really is no reason (mathematically nor import graphically) to have OrderedCancelCommMonoid be defined in a separate file from OrderedCommMonoid.

Also take the opportunity to:

• make OrderedCancelCommMonoid extend OrderedCommMonoid
• fix capitalisation in instance names
• standardise to defining the additive of each structure version first, so that to_additive can be called directly on the multiplicative version
• inline at no cost a few auxiliary lemmas

@@ -247,9 +247,7 @@ theorem mul {x y : K_hat R K} (hx : x.IsFiniteAdele) (hy : y.IsFiniteAdele) :
     have h_mul : Valued.v (x v * y v) = Valued.v (x v) * Valued.v (y v) :=
       Valued.v.map_mul' (x v) (y v)
     rw [mem_adicCompletionIntegers, Pi.mul_apply, h_mul]
-    exact
-      @mul_le_one' (WithZero (Multiplicative ℤ)) _ _ (OrderedCommMonoid.to_covariantClass_left _) _
-        _ hv.left hv.right
+    exact mul_le_one' hv.left hv.right
   exact (hx.union hy).subset h_subset
 #align dedekind_domain.prod_adic_completions.is_finite_adele.mul DedekindDomain.ProdAdicCompletions.IsFiniteAdele.mul
 

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -214,7 +214,6 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele := by
     have h_zero : (Valued.v (0 : v.adicCompletion K) : WithZero (Multiplicative ℤ)) = 0 :=
       Valued.v.map_zero'
     rw [h_zero]; exact zero_le_one' _
-  simp_rw [Pi.zero_apply, h_empty]
   -- Porting note: was `exact`, but `OfNat` got in the way.
   convert finite_empty
 #align dedekind_domain.prod_adic_completions.is_finite_adele.zero DedekindDomain.ProdAdicCompletions.IsFiniteAdele.zero
@@ -262,7 +261,6 @@ theorem one : (1 : K_hat R K).IsFiniteAdele := by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
     rw [mem_setOf] at hv; apply hv; rw [mem_adicCompletionIntegers]
     exact le_of_eq Valued.v.map_one'
-  simp_rw [Pi.one_apply, h_empty]
   -- Porting note: was `exact`, but `OfNat` got in the way.
   convert finite_empty
 #align dedekind_domain.prod_adic_completions.is_finite_adele.one DedekindDomain.ProdAdicCompletions.IsFiniteAdele.one

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ open Function Set IsDedekindDomain IsDedekindDomain.HeightOneSpectrum
 
 namespace DedekindDomain
 
-variable (R K : Type _) [CommRing R] [IsDomain R] [IsDedekindDomain R] [Field K] [Algebra R K]
+variable (R K : Type*) [CommRing R] [IsDomain R] [IsDedekindDomain R] [Field K] [Algebra R K]
   [IsFractionRing R K] (v : HeightOneSpectrum R)
 
 /-- The product of all `adicCompletionIntegers`, where `v` runs over the maximal ideals of `R`. -/

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: María Inés de Frutos-Fernández
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.finite_adele_ring
-! 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.AdicValuation
 
+#align_import ring_theory.dedekind_domain.finite_adele_ring from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # The finite adèle ring of a Dedekind domain
 We define the ring of finite adèles of a Dedekind domain `R`.

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

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

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

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

@@ -213,7 +213,7 @@ theorem zero : (0 : K_hat R K).IsFiniteAdele := by
   have h_empty :
     {v : HeightOneSpectrum R | ¬(0 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ := by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_setOf] at hv ; apply hv; rw [mem_adicCompletionIntegers]
+    rw [mem_setOf] at hv; apply hv; rw [mem_adicCompletionIntegers]
     have h_zero : (Valued.v (0 : v.adicCompletion K) : WithZero (Multiplicative ℤ)) = 0 :=
       Valued.v.map_zero'
     rw [h_zero]; exact zero_le_one' _
@@ -263,7 +263,7 @@ theorem one : (1 : K_hat R K).IsFiniteAdele := by
   have h_empty :
     {v : HeightOneSpectrum R | ¬(1 : v.adicCompletion K) ∈ v.adicCompletionIntegers K} = ∅ := by
     ext v; rw [mem_empty_iff_false, iff_false_iff]; intro hv
-    rw [mem_setOf] at hv ; apply hv; rw [mem_adicCompletionIntegers]
+    rw [mem_setOf] at hv; apply hv; rw [mem_adicCompletionIntegers]
     exact le_of_eq Valued.v.map_one'
   simp_rw [Pi.one_apply, h_empty]
   -- Porting note: was `exact`, but `OfNat` got in the way.