ring_theory.dedekind_domain.S_integer
⟷
Mathlib.RingTheory.DedekindDomain.SInteger
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -62,8 +62,8 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/-! ## `S`-integers -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer /-
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
@@ -76,7 +76,7 @@ def integer : Subalgebra R K :=
#align set.integer Set.integer
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer_eq /-
theorem integer_eq :
(S.integer K).toSubring =
@@ -95,8 +95,8 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
/-! ## `S`-units -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit /-
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
@@ -107,7 +107,7 @@ def unit : Subgroup Kˣ :=
#align set.unit Set.unit
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit_eq /-
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
-import Mathbin.RingTheory.DedekindDomain.AdicValuation
+import RingTheory.DedekindDomain.AdicValuation
#align_import ring_theory.dedekind_domain.S_integer from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
@@ -62,8 +62,8 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/-! ## `S`-integers -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer /-
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
@@ -76,7 +76,7 @@ def integer : Subalgebra R K :=
#align set.integer Set.integer
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer_eq /-
theorem integer_eq :
(S.integer K).toSubring =
@@ -95,8 +95,8 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
/-! ## `S`-units -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit /-
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
@@ -107,7 +107,7 @@ def unit : Subgroup Kˣ :=
#align set.unit Set.unit
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit_eq /-
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.S_integer
-! 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.S_integer from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
+
/-!
# `S`-integers and `S`-units of fraction fields of Dedekind domains
@@ -65,8 +62,8 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/-! ## `S`-integers -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer /-
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
@@ -79,7 +76,7 @@ def integer : Subalgebra R K :=
#align set.integer Set.integer
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.integer_eq /-
theorem integer_eq :
(S.integer K).toSubring =
@@ -98,8 +95,8 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
/-! ## `S`-units -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit /-
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
@@ -110,7 +107,7 @@ def unit : Subgroup Kˣ :=
#align set.unit Set.unit
-/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
#print Set.unit_eq /-
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
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: David Kurniadi Angdinata
! This file was ported from Lean 3 source module ring_theory.dedekind_domain.S_integer
-! leanprover-community/mathlib commit 00ab77614e085c9ef49479babba1a7d826d3232e
+! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.DedekindDomain.AdicValuation
/-!
# `S`-integers and `S`-units of fraction fields of Dedekind domains
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Let `K` be the field of fractions of a Dedekind domain `R`, and let `S` be a set of prime ideals in
the height one spectrum of `R`. An `S`-integer of `K` is defined to have `v`-adic valuation at most
one for all primes ideals `v` away from `S`, whereas an `S`-unit of `Kˣ` is defined to have `v`-adic
mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb
@@ -64,6 +64,7 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+#print Set.integer /-
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
def integer : Subalgebra R K :=
@@ -73,24 +74,30 @@ def integer : Subalgebra R K :=
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subring.mem_iInf] with
algebraMap_mem' := fun x v _ => v.valuation_le_one x }
#align set.integer Set.integer
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+#print Set.integer_eq /-
theorem integer_eq :
(S.integer K).toSubring =
⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.toSubring :=
SetLike.ext' <| by simpa only [integer, Subring.copy_eq]
#align set.integer_eq Set.integer_eq
+-/
+#print Set.integer_valuation_le_one /-
theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv : v ∉ S) :
v.Valuation (x : K) ≤ 1 :=
x.property v hv
#align set.integer_valuation_le_one Set.integer_valuation_le_one
+-/
/-! ## `S`-units -/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+#print Set.unit /-
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
def unit : Subgroup Kˣ :=
@@ -98,18 +105,24 @@ def unit : Subgroup Kˣ :=
{x : Kˣ | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation (x : K) = 1} <|
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_iInf, Valuation.mem_unitGroup_iff]
#align set.unit Set.unit
+-/
/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+#print Set.unit_eq /-
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
Subgroup.copy_eq _ _ _
#align set.unit_eq Set.unit_eq
+-/
+#print Set.unit_valuation_eq_one /-
theorem unit_valuation_eq_one (x : S.Unit K) {v : HeightOneSpectrum R} (hv : v ∉ S) :
v.Valuation (x : K) = 1 :=
x.property v hv
#align set.unit_valuation_eq_one Set.unit_valuation_eq_one
+-/
+#print Set.unitEquivUnitsInteger /-
/-- The group of `S`-units is the group of units of the ring of `S`-integers. -/
@[simps]
def unitEquivUnitsInteger : S.Unit K ≃* (S.integer K)ˣ
@@ -126,6 +139,7 @@ def unitEquivUnitsInteger : S.Unit K ≃* (S.integer K)ˣ
right_inv _ := by ext; rfl
map_mul' _ _ := by ext; rfl
#align set.unit_equiv_units_integer Set.unitEquivUnitsInteger
+-/
end Set
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -62,8 +62,8 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/-! ## `S`-integers -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
def integer : Subalgebra R K :=
@@ -74,7 +74,7 @@ def integer : Subalgebra R K :=
algebraMap_mem' := fun x v _ => v.valuation_le_one x }
#align set.integer Set.integer
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
theorem integer_eq :
(S.integer K).toSubring =
⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.toSubring :=
@@ -89,8 +89,8 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
/-! ## `S`-units -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
def unit : Subgroup Kˣ :=
@@ -99,7 +99,7 @@ def unit : Subgroup Kˣ :=
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_iInf, Valuation.mem_unitGroup_iff]
#align set.unit Set.unit
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ∉ » S) -/
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
Subgroup.copy_eq _ _ _
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -69,7 +69,7 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
def integer : Subalgebra R K :=
{
(⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.toSubring).copy
- { x : K | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation x ≤ 1 } <|
+ {x : K | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation x ≤ 1} <|
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subring.mem_iInf] with
algebraMap_mem' := fun x v _ => v.valuation_le_one x }
#align set.integer Set.integer
@@ -95,7 +95,7 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
@[simps]
def unit : Subgroup Kˣ :=
(⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup).copy
- { x : Kˣ | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation (x : K) = 1 } <|
+ {x : Kˣ | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation (x : K) = 1} <|
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_iInf, Valuation.mem_unitGroup_iff]
#align set.unit Set.unit
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -52,7 +52,7 @@ noncomputable section
open IsDedekindDomain
-open nonZeroDivisors
+open scoped nonZeroDivisors
universe u v
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -120,19 +120,11 @@ def unitEquivUnitsInteger : S.Unit K ≃* (S.integer K)ˣ
invFun x :=
⟨Units.mk0 x fun hx => x.NeZero ((Subring.coe_eq_zero_iff _).mp hx), fun v hv =>
eq_one_of_one_le_mul_left (x.val.property v hv) (x.inv.property v hv) <|
- Eq.ge <| by
- rw [← map_mul]
- convert v.valuation.map_one
+ Eq.ge <| by rw [← map_mul]; convert v.valuation.map_one;
exact subtype.mk_eq_mk.mp x.val_inv⟩
- left_inv _ := by
- ext
- rfl
- right_inv _ := by
- ext
- rfl
- map_mul' _ _ := by
- ext
- rfl
+ left_inv _ := by ext; rfl
+ right_inv _ := by ext; rfl
+ map_mul' _ _ := by ext; rfl
#align set.unit_equiv_units_integer Set.unitEquivUnitsInteger
end Set
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -70,7 +70,7 @@ def integer : Subalgebra R K :=
{
(⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.toSubring).copy
{ x : K | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation x ≤ 1 } <|
- Set.ext fun _ => by simpa only [SetLike.mem_coe, Subring.mem_infᵢ] with
+ Set.ext fun _ => by simpa only [SetLike.mem_coe, Subring.mem_iInf] with
algebraMap_mem' := fun x v _ => v.valuation_le_one x }
#align set.integer Set.integer
@@ -96,7 +96,7 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
def unit : Subgroup Kˣ :=
(⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup).copy
{ x : Kˣ | ∀ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation (x : K) = 1 } <|
- Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_infᵢ, Valuation.mem_unitGroup_iff]
+ Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_iInf, Valuation.mem_unitGroup_iff]
#align set.unit Set.unit
/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -62,8 +62,8 @@ variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
/-! ## `S`-integers -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
/-- The `R`-subalgebra of `S`-integers of `K`. -/
@[simps]
def integer : Subalgebra R K :=
@@ -74,7 +74,7 @@ def integer : Subalgebra R K :=
algebraMap_mem' := fun x v _ => v.valuation_le_one x }
#align set.integer Set.integer
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
theorem integer_eq :
(S.integer K).toSubring =
⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.toSubring :=
@@ -89,8 +89,8 @@ theorem integer_valuation_le_one (x : S.integer K) {v : HeightOneSpectrum R} (hv
/-! ## `S`-units -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
/-- The subgroup of `S`-units of `Kˣ`. -/
@[simps]
def unit : Subgroup Kˣ :=
@@ -99,7 +99,7 @@ def unit : Subgroup Kˣ :=
Set.ext fun _ => by simpa only [SetLike.mem_coe, Subgroup.mem_infᵢ, Valuation.mem_unitGroup_iff]
#align set.unit Set.unit
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ∉ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ∉ » S) -/
theorem unit_eq :
S.Unit K = ⨅ (v) (_ : v ∉ S), (v : HeightOneSpectrum R).Valuation.ValuationSubring.unitGroup :=
Subgroup.copy_eq _ _ _
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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.
@@ -53,7 +53,7 @@ open scoped nonZeroDivisors
universe u v
-variable {R : Type u} [CommRing R] [IsDomain R] [IsDedekindDomain R]
+variable {R : Type u} [CommRing R] [IsDedekindDomain R]
(S : Set <| HeightOneSpectrum R) (K : Type v) [Field K] [Algebra R K] [IsFractionRing R K]
/-! ## `S`-integers -/
@@ -2,14 +2,11 @@
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-
-! This file was ported from Lean 3 source module ring_theory.dedekind_domain.S_integer
-! leanprover-community/mathlib commit 00ab77614e085c9ef49479babba1a7d826d3232e
-! 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.S_integer from "leanprover-community/mathlib"@"00ab77614e085c9ef49479babba1a7d826d3232e"
+
/-!
# `S`-integers and `S`-units of fraction fields of Dedekind domains
The unported dependencies are