algebra.group_with_zero.divisibility | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

e8638a0f

(last sync)

feat(algebra/divisibility/basic): Dot notation aliases (#18698)

A few convenience shortcuts for dvd along with some simple nat lemmas. Also

Drop neg_dvd_of_dvd/dvd_of_neg_dvd/dvd_neg_of_dvd/dvd_of_dvd_neg in favor of the aforementioned shortcuts.
Remove explicit arguments to dvd_neg/neg_dvd.
Drop int.of_nat_dvd_of_dvd_nat_abs/int.dvd_nat_abs_of_of_nat_dvd because they are the two directions of int.coe_nat_dvd_left.
Move group_with_zero.to_cancel_monoid_with_zero from algebra.group_with_zero.units.basic back to algebra.group_with_zero.basic. It was erroneously moved during the Great Splits.

Diff

@@ -88,3 +88,28 @@ begin
 end
 
 end monoid_with_zero
+
+section cancel_comm_monoid_with_zero
+variables [cancel_comm_monoid_with_zero α] [subsingleton αˣ] {a b : α}
+
+lemma dvd_antisymm : a ∣ b → b ∣ a → a = b :=
+begin
+  rintro ⟨c, rfl⟩ ⟨d, hcd⟩,
+  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd,
+  obtain ⟨rfl, -⟩ | rfl := hcd; simp,
+end
+
+attribute [protected] nat.dvd_antisymm --This lemma is in core, so we protect it here
+
+lemma dvd_antisymm' : a ∣ b → b ∣ a → b = a := flip dvd_antisymm
+
+alias dvd_antisymm ← has_dvd.dvd.antisymm
+alias dvd_antisymm' ← has_dvd.dvd.antisymm'
+
+lemma eq_of_forall_dvd (h : ∀ c, a ∣ c ↔ b ∣ c) : a = b :=
+((h _).2 dvd_rfl).antisymm $ (h _).1 dvd_rfl
+
+lemma eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
+((h _).1 dvd_rfl).antisymm $ (h _).2 dvd_rfl
+
+end cancel_comm_monoid_with_zero

f1a2caaf

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

e8638a0f

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -136,7 +136,7 @@ variable [CancelCommMonoidWithZero α] [Subsingleton αˣ] {a b : α}
 theorem dvd_antisymm : a ∣ b → b ∣ a → a = b :=
   by
   rintro ⟨c, rfl⟩ ⟨d, hcd⟩
-  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd 
+  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd
   obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
 #align dvd_antisymm dvd_antisymm
 -/

e8638a0f

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
 Neil Strickland, Aaron Anderson
 -/
-import Mathbin.Algebra.GroupWithZero.Basic
-import Mathbin.Algebra.Divisibility.Units
+import Algebra.GroupWithZero.Basic
+import Algebra.Divisibility.Units
 
 #align_import algebra.group_with_zero.divisibility from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"

e8638a0f

bump to nightly-2023-08-23-23

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

f612b9e0

Diff

@@ -150,10 +150,10 @@ theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=
 #align dvd_antisymm' dvd_antisymm'
 -/
 
-alias dvd_antisymm ← Dvd.dvd.antisymm
+alias Dvd.dvd.antisymm := dvd_antisymm
 #align has_dvd.dvd.antisymm Dvd.dvd.antisymm
 
-alias dvd_antisymm' ← Dvd.dvd.antisymm'
+alias Dvd.dvd.antisymm' := dvd_antisymm'
 #align has_dvd.dvd.antisymm' Dvd.dvd.antisymm'
 
 #print eq_of_forall_dvd /-

e8638a0f

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -3,15 +3,12 @@ Copyright (c) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
 Neil Strickland, Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.group_with_zero.divisibility
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.GroupWithZero.Basic
 import Mathbin.Algebra.Divisibility.Units
 
+#align_import algebra.group_with_zero.divisibility from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Divisibility in groups with zero.

e8638a0f

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -29,37 +29,47 @@ section SemigroupWithZero
 
 variable [SemigroupWithZero α] {a : α}
 
+#print eq_zero_of_zero_dvd /-
 theorem eq_zero_of_zero_dvd (h : 0 ∣ a) : a = 0 :=
   Dvd.elim h fun c H' => H'.trans (MulZeroClass.zero_mul c)
 #align eq_zero_of_zero_dvd eq_zero_of_zero_dvd
+-/
 
+#print zero_dvd_iff /-
 /-- Given an element `a` of a commutative semigroup with zero, there exists another element whose
     product with zero equals `a` iff `a` equals zero. -/
 @[simp]
 theorem zero_dvd_iff : 0 ∣ a ↔ a = 0 :=
   ⟨eq_zero_of_zero_dvd, fun h => by rw [h]; use 0; simp⟩
 #align zero_dvd_iff zero_dvd_iff
+-/
 
+#print dvd_zero /-
 @[simp]
 theorem dvd_zero (a : α) : a ∣ 0 :=
   Dvd.intro 0 (by simp)
 #align dvd_zero dvd_zero
+-/
 
 end SemigroupWithZero
 
+#print mul_dvd_mul_iff_left /-
 /-- Given two elements `b`, `c` of a `cancel_monoid_with_zero` and a nonzero element `a`,
  `a*b` divides `a*c` iff `b` divides `c`. -/
 theorem mul_dvd_mul_iff_left [CancelMonoidWithZero α] {a b c : α} (ha : a ≠ 0) :
     a * b ∣ a * c ↔ b ∣ c :=
   exists_congr fun d => by rw [mul_assoc, mul_right_inj' ha]
 #align mul_dvd_mul_iff_left mul_dvd_mul_iff_left
+-/
 
+#print mul_dvd_mul_iff_right /-
 /-- Given two elements `a`, `b` of a commutative `cancel_monoid_with_zero` and a nonzero
   element `c`, `a*c` divides `b*c` iff `a` divides `b`. -/
 theorem mul_dvd_mul_iff_right [CancelCommMonoidWithZero α] {a b c : α} (hc : c ≠ 0) :
     a * c ∣ b * c ↔ a ∣ b :=
   exists_congr fun d => by rw [mul_right_comm, mul_left_inj' hc]
 #align mul_dvd_mul_iff_right mul_dvd_mul_iff_right
+-/
 
 section CommMonoidWithZero
 
@@ -111,11 +121,13 @@ section MonoidWithZero
 
 variable [MonoidWithZero α]
 
+#print ne_zero_of_dvd_ne_zero /-
 theorem ne_zero_of_dvd_ne_zero {p q : α} (h₁ : q ≠ 0) (h₂ : p ∣ q) : p ≠ 0 :=
   by
   rcases h₂ with ⟨u, rfl⟩
   exact left_ne_zero_of_mul h₁
 #align ne_zero_of_dvd_ne_zero ne_zero_of_dvd_ne_zero
+-/
 
 end MonoidWithZero

e8638a0f

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -127,7 +127,7 @@ variable [CancelCommMonoidWithZero α] [Subsingleton αˣ] {a b : α}
 theorem dvd_antisymm : a ∣ b → b ∣ a → a = b :=
   by
   rintro ⟨c, rfl⟩ ⟨d, hcd⟩
-  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd
+  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd 
   obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
 #align dvd_antisymm dvd_antisymm
 -/

e8638a0f

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -29,22 +29,10 @@ section SemigroupWithZero
 
 variable [SemigroupWithZero α] {a : α}
 
-/- warning: eq_zero_of_zero_dvd -> eq_zero_of_zero_dvd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] {a : α}, (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (SemigroupWithZero.toMulZeroClass.{u1} α _inst_1))))) a) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (SemigroupWithZero.toMulZeroClass.{u1} α _inst_1))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] {a : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))) a) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_zero_of_zero_dvd eq_zero_of_zero_dvdₓ'. -/
 theorem eq_zero_of_zero_dvd (h : 0 ∣ a) : a = 0 :=
   Dvd.elim h fun c H' => H'.trans (MulZeroClass.zero_mul c)
 #align eq_zero_of_zero_dvd eq_zero_of_zero_dvd
 
-/- warning: zero_dvd_iff -> zero_dvd_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] {a : α}, Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (SemigroupWithZero.toMulZeroClass.{u1} α _inst_1))))) a) (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (SemigroupWithZero.toMulZeroClass.{u1} α _inst_1))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] {a : α}, Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))) a) (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align zero_dvd_iff zero_dvd_iffₓ'. -/
 /-- Given an element `a` of a commutative semigroup with zero, there exists another element whose
     product with zero equals `a` iff `a` equals zero. -/
 @[simp]
@@ -52,12 +40,6 @@ theorem zero_dvd_iff : 0 ∣ a ↔ a = 0 :=
   ⟨eq_zero_of_zero_dvd, fun h => by rw [h]; use 0; simp⟩
 #align zero_dvd_iff zero_dvd_iff
 
-/- warning: dvd_zero -> dvd_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] (a : α), Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (SemigroupWithZero.toMulZeroClass.{u1} α _inst_1)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] (a : α), Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align dvd_zero dvd_zeroₓ'. -/
 @[simp]
 theorem dvd_zero (a : α) : a ∣ 0 :=
   Dvd.intro 0 (by simp)
@@ -65,12 +47,6 @@ theorem dvd_zero (a : α) : a ∣ 0 :=
 
 end SemigroupWithZero
 
-/- warning: mul_dvd_mul_iff_left -> mul_dvd_mul_iff_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))))))) -> (Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))) a c)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) b c))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelMonoidWithZero.{u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))) -> (Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1))))) a c)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CancelMonoidWithZero.toMonoidWithZero.{u1} α _inst_1)))) b c))
-Case conversion may be inaccurate. Consider using '#align mul_dvd_mul_iff_left mul_dvd_mul_iff_leftₓ'. -/
 /-- Given two elements `b`, `c` of a `cancel_monoid_with_zero` and a nonzero element `a`,
  `a*b` divides `a*c` iff `b` divides `c`. -/
 theorem mul_dvd_mul_iff_left [CancelMonoidWithZero α] {a b c : α} (ha : a ≠ 0) :
@@ -78,12 +54,6 @@ theorem mul_dvd_mul_iff_left [CancelMonoidWithZero α] {a b c : α} (ha : a ≠
   exists_congr fun d => by rw [mul_assoc, mul_right_inj' ha]
 #align mul_dvd_mul_iff_left mul_dvd_mul_iff_left
 
-/- warning: mul_dvd_mul_iff_right -> mul_dvd_mul_iff_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))))))) -> (Iff (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toHasMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b c)) (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} α] {a : α} {b : α} {c : α}, (Ne.{succ u1} α c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) -> (Iff (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulZeroClass.toMul.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1)))))) b c)) (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α (CommMonoidWithZero.toMonoidWithZero.{u1} α (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align mul_dvd_mul_iff_right mul_dvd_mul_iff_rightₓ'. -/
 /-- Given two elements `a`, `b` of a commutative `cancel_monoid_with_zero` and a nonzero
   element `c`, `a*c` divides `b*c` iff `a` divides `b`. -/
 theorem mul_dvd_mul_iff_right [CancelCommMonoidWithZero α] {a b c : α} (hc : c ≠ 0) :
@@ -141,12 +111,6 @@ section MonoidWithZero
 
 variable [MonoidWithZero α]
 
-/- warning: ne_zero_of_dvd_ne_zero -> ne_zero_of_dvd_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} α] {p : α} {q : α}, (Ne.{succ u1} α q (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α _inst_1))))))) -> (Dvd.Dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α _inst_1))) p q) -> (Ne.{succ u1} α p (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (MulZeroOneClass.toMulZeroClass.{u1} α (MonoidWithZero.toMulZeroOneClass.{u1} α _inst_1)))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MonoidWithZero.{u1} α] {p : α} {q : α}, (Ne.{succ u1} α q (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α _inst_1)))) -> (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α (MonoidWithZero.toSemigroupWithZero.{u1} α _inst_1))) p q) -> (Ne.{succ u1} α p (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (MonoidWithZero.toZero.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align ne_zero_of_dvd_ne_zero ne_zero_of_dvd_ne_zeroₓ'. -/
 theorem ne_zero_of_dvd_ne_zero {p q : α} (h₁ : q ≠ 0) (h₂ : p ∣ q) : p ≠ 0 :=
   by
   rcases h₂ with ⟨u, rfl⟩

e8638a0f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -49,10 +49,7 @@ Case conversion may be inaccurate. Consider using '#align zero_dvd_iff zero_dvd_
     product with zero equals `a` iff `a` equals zero. -/
 @[simp]
 theorem zero_dvd_iff : 0 ∣ a ↔ a = 0 :=
-  ⟨eq_zero_of_zero_dvd, fun h => by
-    rw [h]
-    use 0
-    simp⟩
+  ⟨eq_zero_of_zero_dvd, fun h => by rw [h]; use 0; simp⟩
 #align zero_dvd_iff zero_dvd_iff
 
 /- warning: dvd_zero -> dvd_zero is a dubious translation:
@@ -110,8 +107,7 @@ def DvdNotUnit (a b : α) : Prop :=
 theorem dvdNotUnit_of_dvd_of_not_dvd {a b : α} (hd : a ∣ b) (hnd : ¬b ∣ a) : DvdNotUnit a b :=
   by
   constructor
-  · rintro rfl
-    exact hnd (dvd_zero _)
+  · rintro rfl; exact hnd (dvd_zero _)
   · rcases hd with ⟨c, rfl⟩
     refine' ⟨c, _, rfl⟩
     rintro ⟨u, rfl⟩

e8638a0f

bump to nightly-2023-04-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

0ff24cd7

Diff

@@ -163,33 +163,41 @@ section CancelCommMonoidWithZero
 
 variable [CancelCommMonoidWithZero α] [Subsingleton αˣ] {a b : α}
 
+#print dvd_antisymm /-
 theorem dvd_antisymm : a ∣ b → b ∣ a → a = b :=
   by
   rintro ⟨c, rfl⟩ ⟨d, hcd⟩
   rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd
   obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
 #align dvd_antisymm dvd_antisymm
+-/
 
 attribute [protected] Nat.dvd_antisymm
 
+#print dvd_antisymm' /-
 --This lemma is in core, so we protect it here
 theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=
   flip dvd_antisymm
 #align dvd_antisymm' dvd_antisymm'
+-/
 
-alias dvd_antisymm ← Dvd.Dvd.antisymm
-#align has_dvd.dvd.antisymm Dvd.Dvd.antisymm
+alias dvd_antisymm ← Dvd.dvd.antisymm
+#align has_dvd.dvd.antisymm Dvd.dvd.antisymm
 
-alias dvd_antisymm' ← Dvd.Dvd.antisymm'
-#align has_dvd.dvd.antisymm' Dvd.Dvd.antisymm'
+alias dvd_antisymm' ← Dvd.dvd.antisymm'
+#align has_dvd.dvd.antisymm' Dvd.dvd.antisymm'
 
+#print eq_of_forall_dvd /-
 theorem eq_of_forall_dvd (h : ∀ c, a ∣ c ↔ b ∣ c) : a = b :=
   ((h _).2 dvd_rfl).antisymm <| (h _).1 dvd_rfl
 #align eq_of_forall_dvd eq_of_forall_dvd
+-/
 
+#print eq_of_forall_dvd' /-
 theorem eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
   ((h _).1 dvd_rfl).antisymm <| (h _).2 dvd_rfl
 #align eq_of_forall_dvd' eq_of_forall_dvd'
+-/
 
 end CancelCommMonoidWithZero

e8638a0f

bump to nightly-2023-04-06-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

89485060

Diff

@@ -5,7 +5,7 @@ Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston,
 Neil Strickland, Aaron Anderson
 
 ! This file was ported from Lean 3 source module algebra.group_with_zero.divisibility
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -159,3 +159,37 @@ theorem ne_zero_of_dvd_ne_zero {p q : α} (h₁ : q ≠ 0) (h₂ : p ∣ q) : p
 
 end MonoidWithZero
 
+section CancelCommMonoidWithZero
+
+variable [CancelCommMonoidWithZero α] [Subsingleton αˣ] {a b : α}
+
+theorem dvd_antisymm : a ∣ b → b ∣ a → a = b :=
+  by
+  rintro ⟨c, rfl⟩ ⟨d, hcd⟩
+  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd
+  obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
+#align dvd_antisymm dvd_antisymm
+
+attribute [protected] Nat.dvd_antisymm
+
+--This lemma is in core, so we protect it here
+theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=
+  flip dvd_antisymm
+#align dvd_antisymm' dvd_antisymm'
+
+alias dvd_antisymm ← Dvd.Dvd.antisymm
+#align has_dvd.dvd.antisymm Dvd.Dvd.antisymm
+
+alias dvd_antisymm' ← Dvd.Dvd.antisymm'
+#align has_dvd.dvd.antisymm' Dvd.Dvd.antisymm'
+
+theorem eq_of_forall_dvd (h : ∀ c, a ∣ c ↔ b ∣ c) : a = b :=
+  ((h _).2 dvd_rfl).antisymm <| (h _).1 dvd_rfl
+#align eq_of_forall_dvd eq_of_forall_dvd
+
+theorem eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
+  ((h _).1 dvd_rfl).antisymm <| (h _).2 dvd_rfl
+#align eq_of_forall_dvd' eq_of_forall_dvd'
+
+end CancelCommMonoidWithZero
+

448144f7

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -36,7 +36,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SemigroupWithZero.{u1} α] {a : α}, (Dvd.dvd.{u1} α (semigroupDvd.{u1} α (SemigroupWithZero.toSemigroup.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))) a) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (SemigroupWithZero.toZero.{u1} α _inst_1))))
 Case conversion may be inaccurate. Consider using '#align eq_zero_of_zero_dvd eq_zero_of_zero_dvdₓ'. -/
 theorem eq_zero_of_zero_dvd (h : 0 ∣ a) : a = 0 :=
-  Dvd.elim h fun c H' => H'.trans (zero_mul c)
+  Dvd.elim h fun c H' => H'.trans (MulZeroClass.zero_mul c)
 #align eq_zero_of_zero_dvd eq_zero_of_zero_dvd
 
 /- warning: zero_dvd_iff -> zero_dvd_iff is a dubious translation:

448144f7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e8638a0f

feat(Algebra/GroupWithZero): remove already existing lemmas (#11691)

Undo #11677 since we have found out that the lemmas

https://github.com/leanprover-community/mathlib4/blob/044f1333d4e273d0d45e7fdeaf07266d7e043c32/Mathlib/Algebra/GroupWithZero/Divisibility.lean#L171-L179

already exist in the same file with different names mul_dvd_mul_iff_left and mul_dvd_mul_iff_right:

https://github.com/leanprover-community/mathlib4/blob/0f2ac6785f4ecb39c798a30eee01dafa63c828d7/Mathlib/Algebra/GroupWithZero/Divisibility.lean#L46-L58

171abc8c

Diff

@@ -168,14 +168,4 @@ theorem eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
   ((h _).1 dvd_rfl).antisymm <| (h _).2 dvd_rfl
 #align eq_of_forall_dvd' eq_of_forall_dvd'
 
-lemma dvd_of_mul_dvd_mul_left {c : α} (hc : c ≠ 0)
-    (H : c * a ∣ c * b) : a ∣ b := by
-  rcases H with ⟨d, hd⟩
-  exact ⟨d, by simpa [mul_assoc, hc] using hd⟩
-
-lemma dvd_of_mul_dvd_mul_right {c : α} (hc : c ≠ 0)
-    (H : a * c ∣ b * c) : a ∣ b := by
-  rw [mul_comm a c, mul_comm b c] at H
-  exact dvd_of_mul_dvd_mul_left hc H
-
 end CancelCommMonoidWithZero

e8638a0f

feat(Algebra/GroupWithZero): add dvd_of_mul_dvd_mul (#11677)

dvd_of_mul_dvd_mul_left and dvd_of_mul_dvd_mul_right were implemented only for Nat and Int.

We've generalised it for CancelCommMonoidWithZero.

f88c5854

Diff

@@ -168,4 +168,14 @@ theorem eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
   ((h _).1 dvd_rfl).antisymm <| (h _).2 dvd_rfl
 #align eq_of_forall_dvd' eq_of_forall_dvd'
 
+lemma dvd_of_mul_dvd_mul_left {c : α} (hc : c ≠ 0)
+    (H : c * a ∣ c * b) : a ∣ b := by
+  rcases H with ⟨d, hd⟩
+  exact ⟨d, by simpa [mul_assoc, hc] using hd⟩
+
+lemma dvd_of_mul_dvd_mul_right {c : α} (hc : c ≠ 0)
+    (H : a * c ∣ b * c) : a ∣ b := by
+  rw [mul_comm a c, mul_comm b c] at H
+  exact dvd_of_mul_dvd_mul_left hc H
+
 end CancelCommMonoidWithZero

e8638a0f

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -147,7 +147,7 @@ theorem dvd_antisymm : a ∣ b → b ∣ a → a = b := by
   obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
 #align dvd_antisymm dvd_antisymm
 
--- porting note: `attribute [protected]` is currently unsupported
+-- Porting note: `attribute [protected]` is currently unsupported
 -- attribute [protected] Nat.dvd_antisymm --This lemma is in core, so we protect it here
 
 theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=

e8638a0f

feat: introduce IsRelPrime and DecompositionMonoid and refactor (#10327)

Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.
Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.
Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.
Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.
Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.
Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

b569e065

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
 Neil Strickland, Aaron Anderson
 -/
-import Mathlib.Algebra.GroupWithZero.Basic
+import Mathlib.Algebra.GroupWithZero.Units.Basic
 import Mathlib.Algebra.Divisibility.Units
 
 #align_import algebra.group_with_zero.divisibility from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
@@ -77,8 +77,27 @@ theorem dvdNotUnit_of_dvd_of_not_dvd {a b : α} (hd : a ∣ b) (hnd : ¬b ∣ a)
     simp at hnd
 #align dvd_not_unit_of_dvd_of_not_dvd dvdNotUnit_of_dvd_of_not_dvd
 
+variable {x y : α}
+
+theorem isRelPrime_zero_left : IsRelPrime 0 x ↔ IsUnit x :=
+  ⟨(· (dvd_zero _) dvd_rfl), IsUnit.isRelPrime_right⟩
+
+theorem isRelPrime_zero_right : IsRelPrime x 0 ↔ IsUnit x :=
+  isRelPrime_comm.trans isRelPrime_zero_left
+
+theorem not_isRelPrime_zero_zero [Nontrivial α] : ¬IsRelPrime (0 : α) 0 :=
+  mt isRelPrime_zero_right.mp not_isUnit_zero
+
+theorem IsRelPrime.ne_zero_or_ne_zero [Nontrivial α] (h : IsRelPrime x y) : x ≠ 0 ∨ y ≠ 0 :=
+  not_or_of_imp <| by rintro rfl rfl; exact not_isRelPrime_zero_zero h
+
 end CommMonoidWithZero
 
+theorem isRelPrime_of_no_nonunits_factors [MonoidWithZero α] {x y : α} (nonzero : ¬(x = 0 ∧ y = 0))
+    (H : ∀ z, ¬ IsUnit z → z ≠ 0 → z ∣ x → ¬z ∣ y) : IsRelPrime x y := by
+  refine fun z hx hy ↦ by_contra fun h ↦ H z h ?_ hx hy
+  rintro rfl; exact nonzero ⟨zero_dvd_iff.1 hx, zero_dvd_iff.1 hy⟩
+
 theorem dvd_and_not_dvd_iff [CancelCommMonoidWithZero α] {x y : α} :
     x ∣ y ∧ ¬y ∣ x ↔ DvdNotUnit x y :=
   ⟨fun ⟨⟨d, hd⟩, hyx⟩ =>
@@ -104,6 +123,18 @@ theorem ne_zero_of_dvd_ne_zero {p q : α} (h₁ : q ≠ 0) (h₂ : p ∣ q) : p
   exact left_ne_zero_of_mul h₁
 #align ne_zero_of_dvd_ne_zero ne_zero_of_dvd_ne_zero
 
+theorem isPrimal_zero : IsPrimal (0 : α) :=
+  fun a b h ↦ ⟨a, b, dvd_rfl, dvd_rfl, (zero_dvd_iff.mp h).symm⟩
+
+theorem IsPrimal.mul {α} [CancelCommMonoidWithZero α] {m n : α}
+    (hm : IsPrimal m) (hn : IsPrimal n) : IsPrimal (m * n) := by
+  obtain rfl | h0 := eq_or_ne m 0; · rwa [zero_mul]
+  intro b c h
+  obtain ⟨a₁, a₂, ⟨b, rfl⟩, ⟨c, rfl⟩, rfl⟩ := hm (dvd_of_mul_right_dvd h)
+  rw [mul_mul_mul_comm, mul_dvd_mul_iff_left h0] at h
+  obtain ⟨a₁', a₂', h₁, h₂, rfl⟩ := hn h
+  exact ⟨a₁ * a₁', a₂ * a₂', mul_dvd_mul_left _ h₁, mul_dvd_mul_left _ h₂, mul_mul_mul_comm _ _ _ _⟩
+
 end MonoidWithZero
 
 section CancelCommMonoidWithZero

e8638a0f

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -123,10 +123,10 @@ theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=
   flip dvd_antisymm
 #align dvd_antisymm' dvd_antisymm'
 
-alias dvd_antisymm ← Dvd.dvd.antisymm
+alias Dvd.dvd.antisymm := dvd_antisymm
 #align has_dvd.dvd.antisymm Dvd.dvd.antisymm
 
-alias dvd_antisymm' ← Dvd.dvd.antisymm'
+alias Dvd.dvd.antisymm' := dvd_antisymm'
 #align has_dvd.dvd.antisymm' Dvd.dvd.antisymm'
 
 theorem eq_of_forall_dvd (h : ∀ c, a ∣ c ↔ b ∣ c) : a = b :=

e8638a0f

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -17,7 +17,7 @@ Lemmas about divisibility in groups and monoids with zero.
 -/
 
 
-variable {α : Type _}
+variable {α : Type*}
 
 section SemigroupWithZero

e8638a0f

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -3,15 +3,12 @@ Copyright (c) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
 Neil Strickland, Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.group_with_zero.divisibility
-! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GroupWithZero.Basic
 import Mathlib.Algebra.Divisibility.Units
 
+#align_import algebra.group_with_zero.divisibility from "leanprover-community/mathlib"@"e8638a0fcaf73e4500469f368ef9494e495099b3"
+
 /-!
 # Divisibility in groups with zero.

e8638a0f

feat: Dot notation aliases (#3303)

Match https://github.com/leanprover-community/mathlib/pull/18698 and a bit of https://github.com/leanprover-community/mathlib/pull/18785.

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

4fa401fa

Diff

@@ -5,7 +5,7 @@ Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston,
 Neil Strickland, Aaron Anderson
 
 ! This file was ported from Lean 3 source module algebra.group_with_zero.divisibility
-! leanprover-community/mathlib commit f1a2caaf51ef593799107fe9a8d5e411599f3996
+! leanprover-community/mathlib commit e8638a0fcaf73e4500469f368ef9494e495099b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -108,3 +108,36 @@ theorem ne_zero_of_dvd_ne_zero {p q : α} (h₁ : q ≠ 0) (h₂ : p ∣ q) : p
 #align ne_zero_of_dvd_ne_zero ne_zero_of_dvd_ne_zero
 
 end MonoidWithZero
+
+section CancelCommMonoidWithZero
+
+variable [CancelCommMonoidWithZero α] [Subsingleton αˣ] {a b : α}
+
+theorem dvd_antisymm : a ∣ b → b ∣ a → a = b := by
+  rintro ⟨c, rfl⟩ ⟨d, hcd⟩
+  rw [mul_assoc, eq_comm, mul_right_eq_self₀, mul_eq_one] at hcd
+  obtain ⟨rfl, -⟩ | rfl := hcd <;> simp
+#align dvd_antisymm dvd_antisymm
+
+-- porting note: `attribute [protected]` is currently unsupported
+-- attribute [protected] Nat.dvd_antisymm --This lemma is in core, so we protect it here
+
+theorem dvd_antisymm' : a ∣ b → b ∣ a → b = a :=
+  flip dvd_antisymm
+#align dvd_antisymm' dvd_antisymm'
+
+alias dvd_antisymm ← Dvd.dvd.antisymm
+#align has_dvd.dvd.antisymm Dvd.dvd.antisymm
+
+alias dvd_antisymm' ← Dvd.dvd.antisymm'
+#align has_dvd.dvd.antisymm' Dvd.dvd.antisymm'
+
+theorem eq_of_forall_dvd (h : ∀ c, a ∣ c ↔ b ∣ c) : a = b :=
+  ((h _).2 dvd_rfl).antisymm <| (h _).1 dvd_rfl
+#align eq_of_forall_dvd eq_of_forall_dvd
+
+theorem eq_of_forall_dvd' (h : ∀ c, c ∣ a ↔ c ∣ b) : a = b :=
+  ((h _).1 dvd_rfl).antisymm <| (h _).2 dvd_rfl
+#align eq_of_forall_dvd' eq_of_forall_dvd'
+
+end CancelCommMonoidWithZero

f1a2caaf

chore: add source headers to ported theory files (#1094)

The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md

f168625e

Diff

@@ -3,6 +3,11 @@ Copyright (c) 2014 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov,
 Neil Strickland, Aaron Anderson
+
+! This file was ported from Lean 3 source module algebra.group_with_zero.divisibility
+! leanprover-community/mathlib commit f1a2caaf51ef593799107fe9a8d5e411599f3996
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.GroupWithZero.Basic
 import Mathlib.Algebra.Divisibility.Units

`algebra.group_with_zero.divisibility` ⟷ `Mathlib.Algebra.GroupWithZero.Divisibility`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 25

algebra.group_with_zero.divisibility ⟷ Mathlib.Algebra.GroupWithZero.Divisibility

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 25

`algebra.group_with_zero.divisibility` ⟷ `Mathlib.Algebra.GroupWithZero.Divisibility`