ring_theory.valuation.integral ⟷
Mathlib.RingTheory.Valuation.Integral
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
@@ -39,7 +39,7 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
let ⟨p, hpm, hpx⟩ := hx
le_of_not_lt fun hvx : 1 < v x =>
by
- rw [hpm.as_sum, eval₂_add, eval₂_pow, eval₂_X, eval₂_finset_sum, add_eq_zero_iff_eq_neg] at hpx
+ rw [hpm.as_sum, eval₂_add, eval₂_pow, eval₂_X, eval₂_finset_sum, add_eq_zero_iff_eq_neg] at hpx
replace hpx := congr_arg v hpx; refine' ne_of_gt _ hpx
rw [v.map_neg, v.map_pow]
refine' v.map_sum_lt' (zero_lt_one.trans_le (one_le_pow_of_one_le' hvx.le _)) fun i hi => _
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -46,8 +46,8 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
rw [eval₂_mul, eval₂_pow, eval₂_C, eval₂_X, v.map_mul, v.map_pow, ←
one_mul (v x ^ p.nat_degree)]
cases' (hv.2 <| p.coeff i).lt_or_eq with hvpi hvpi
- · exact mul_lt_mul₀ hvpi (pow_lt_pow₀ hvx <| Finset.mem_range.1 hi)
- · erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow₀ hvx (Finset.mem_range.1 hi)
+ · exact mul_lt_mul₀ hvpi (pow_lt_pow_right₀ hvx <| Finset.mem_range.1 hi)
+ · erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow_right₀ hvx (Finset.mem_range.1 hi)
#align valuation.integers.mem_of_integral Valuation.Integers.mem_of_integral
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
-import Mathbin.RingTheory.IntegrallyClosed
-import Mathbin.RingTheory.Valuation.Integers
+import RingTheory.IntegrallyClosed
+import RingTheory.Valuation.Integers
#align_import ring_theory.valuation.integral from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.valuation.integral
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.RingTheory.IntegrallyClosed
import Mathbin.RingTheory.Valuation.Integers
+#align_import ring_theory.valuation.integral from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
/-!
# Integral elements over the ring of integers of a valution
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -35,10 +35,9 @@ variable {R : Type u} {Γ₀ : Type v} [CommRing R] [LinearOrderedCommGroupWithZ
variable {v : Valuation R Γ₀} {O : Type w} [CommRing O] [Algebra O R] (hv : Integers v O)
-include hv
-
open Polynomial
+#print Valuation.Integers.mem_of_integral /-
theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
let ⟨p, hpm, hpx⟩ := hx
le_of_not_lt fun hvx : 1 < v x =>
@@ -53,12 +52,15 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
· exact mul_lt_mul₀ hvpi (pow_lt_pow₀ hvx <| Finset.mem_range.1 hi)
· erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow₀ hvx (Finset.mem_range.1 hi)
#align valuation.integers.mem_of_integral Valuation.Integers.mem_of_integral
+-/
+#print Valuation.Integers.integralClosure /-
protected theorem integralClosure : integralClosure O R = ⊥ :=
bot_unique fun r hr =>
let ⟨x, hx⟩ := hv.3 (hv.mem_of_integral hr)
Algebra.mem_bot.2 ⟨x, hx⟩
#align valuation.integers.integral_closure Valuation.Integers.integralClosure
+-/
end CommRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
! This file was ported from Lean 3 source module ring_theory.valuation.integral
-! leanprover-community/mathlib commit 9b2660e1b25419042c8da10bf411aa3c67f14383
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
! 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.Valuation.Integers
/-!
# Integral elements over the ring of integers of a valution
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The ring of integers is integrally closed inside the original ring.
-/
@@ -69,9 +72,11 @@ variable [Algebra O K] [IsFractionRing O K]
variable (hv : Integers v O)
+#print Valuation.Integers.integrallyClosed /-
theorem integrallyClosed : IsIntegrallyClosed O :=
(IsIntegrallyClosed.integralClosure_eq_bot_iff K).mp (Valuation.Integers.integralClosure hv)
#align valuation.integers.integrally_closed Valuation.Integers.integrallyClosed
+-/
end FractionField
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -40,7 +40,7 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
let ⟨p, hpm, hpx⟩ := hx
le_of_not_lt fun hvx : 1 < v x =>
by
- rw [hpm.as_sum, eval₂_add, eval₂_pow, eval₂_X, eval₂_finset_sum, add_eq_zero_iff_eq_neg] at hpx
+ rw [hpm.as_sum, eval₂_add, eval₂_pow, eval₂_X, eval₂_finset_sum, add_eq_zero_iff_eq_neg] at hpx
replace hpx := congr_arg v hpx; refine' ne_of_gt _ hpx
rw [v.map_neg, v.map_pow]
refine' v.map_sum_lt' (zero_lt_one.trans_le (one_le_pow_of_one_le' hvx.le _)) fun i hi => _
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -20,7 +20,7 @@ The ring of integers is integrally closed inside the original ring.
universe u v w
-open BigOperators
+open scoped BigOperators
namespace Valuation
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -48,9 +48,7 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
one_mul (v x ^ p.nat_degree)]
cases' (hv.2 <| p.coeff i).lt_or_eq with hvpi hvpi
· exact mul_lt_mul₀ hvpi (pow_lt_pow₀ hvx <| Finset.mem_range.1 hi)
- · erw [hvpi]
- rw [one_mul, one_mul]
- exact pow_lt_pow₀ hvx (Finset.mem_range.1 hi)
+ · erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow₀ hvx (Finset.mem_range.1 hi)
#align valuation.integers.mem_of_integral Valuation.Integers.mem_of_integral
protected theorem integralClosure : integralClosure O R = ⊥ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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)
@@ -26,7 +26,6 @@ namespace Integers
section CommRing
variable {R : Type u} {Γ₀ : Type v} [CommRing R] [LinearOrderedCommGroupWithZero Γ₀]
-
variable {v : Valuation R Γ₀} {O : Type w} [CommRing O] [Algebra O R] (hv : Integers v O)
open Polynomial
@@ -56,11 +55,8 @@ end CommRing
section FractionField
variable {K : Type u} {Γ₀ : Type v} [Field K] [LinearOrderedCommGroupWithZero Γ₀]
-
variable {v : Valuation K Γ₀} {O : Type w} [CommRing O] [IsDomain O]
-
variable [Algebra O K] [IsFractionRing O K]
-
variable (hv : Integers v O)
theorem integrallyClosed : IsIntegrallyClosed O :=
The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.
Algebra.GroupPower.Orderpow_mono → pow_right_monopow_le_pow → pow_le_pow_rightpow_le_pow_of_le_left → pow_le_pow_leftpow_lt_pow_of_lt_left → pow_lt_pow_leftstrictMonoOn_pow → pow_left_strictMonoOnpow_strictMono_right → pow_right_strictMonopow_lt_pow → pow_lt_pow_rightpow_lt_pow_iff → pow_lt_pow_iff_rightpow_le_pow_iff → pow_le_pow_iff_rightself_lt_pow → lt_self_powstrictAnti_pow → pow_right_strictAntipow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_onepow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_onelt_of_pow_lt_pow → lt_of_pow_lt_pow_leftle_of_pow_le_pow → le_of_pow_le_pow_leftpow_lt_pow₀ → pow_lt_pow_right₀Algebra.GroupPower.CovariantClasspow_le_pow_of_le_left' → pow_le_pow_left'nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_rightpow_lt_pow' → pow_lt_pow_right'nsmul_lt_nsmul → nsmul_lt_nsmul_leftpow_strictMono_left → pow_right_strictMono'nsmul_strictMono_right → nsmul_left_strictMonoStrictMono.pow_right' → StrictMono.pow_constStrictMono.nsmul_left → StrictMono.const_nsmulpow_strictMono_right' → pow_left_strictMononsmul_strictMono_left → nsmul_right_strictMonoMonotone.pow_right → Monotone.pow_constMonotone.nsmul_left → Monotone.const_nsmullt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_rightpow_le_pow' → pow_le_pow_right'nsmul_le_nsmul → nsmul_le_nsmul_leftpow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonposle_of_pow_le_pow' → le_of_pow_le_pow_left'le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'pow_le_pow_iff' → pow_le_pow_iff_right'nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_leftpow_lt_pow_iff' → pow_lt_pow_iff_right'nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_leftData.Nat.PowNat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_leftNat.pow_le_iff_le_left → Nat.pow_le_pow_iff_leftNat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_leftpow_le_pow_iff_leftpow_lt_pow_iff_leftpow_right_injectivepow_right_injNat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.self_le_pow was a duplicate of le_self_pow.Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.Nat.pow_right_strictMono is defeq to pow_right_strictMono.Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.0 < n or 1 ≤ n to n ≠ 0.Nat lemmas have been protected.@@ -41,8 +41,8 @@ theorem mem_of_integral {x : R} (hx : IsIntegral O x) : x ∈ v.integer :=
rw [eval₂_mul, eval₂_pow, eval₂_C, eval₂_X, v.map_mul, v.map_pow, ←
one_mul (v x ^ p.natDegree)]
cases' (hv.2 <| p.coeff i).lt_or_eq with hvpi hvpi
- · exact mul_lt_mul₀ hvpi (pow_lt_pow₀ hvx <| Finset.mem_range.1 hi)
- · erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow₀ hvx (Finset.mem_range.1 hi)
+ · exact mul_lt_mul₀ hvpi (pow_lt_pow_right₀ hvx <| Finset.mem_range.1 hi)
+ · erw [hvpi]; rw [one_mul, one_mul]; exact pow_lt_pow_right₀ hvx (Finset.mem_range.1 hi)
#align valuation.integers.mem_of_integral Valuation.Integers.mem_of_integral
protected theorem integralClosure : integralClosure O R = ⊥ :=
@@ -2,15 +2,12 @@
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.valuation.integral
-! leanprover-community/mathlib commit 9b2660e1b25419042c8da10bf411aa3c67f14383
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.IntegrallyClosed
import Mathlib.RingTheory.Valuation.Integers
+#align_import ring_theory.valuation.integral from "leanprover-community/mathlib"@"9b2660e1b25419042c8da10bf411aa3c67f14383"
+
/-!
# Integral elements over the ring of integers of a valuation
@@ -12,7 +12,7 @@ import Mathlib.RingTheory.IntegrallyClosed
import Mathlib.RingTheory.Valuation.Integers
/-!
-# Integral elements over the ring of integers of a valution
+# Integral elements over the ring of integers of a valuation
The ring of integers is integrally closed inside the original ring.
-/
The unported dependencies are