ring_theory.prime | 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

008205aa

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

327c3c0d

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -36,7 +36,7 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
   by
   induction' s using Finset.induction with i s his ih generalizing x y a
   · exact ⟨∅, ∅, x, y, by simp [hx]⟩
-  · rw [prod_insert his, ← mul_assoc] at hx 
+  · rw [prod_insert his, ← mul_assoc] at hx
     have hpi : Prime (p i) := hp i (mem_insert_self _ _)
     rcases ih (fun i hi => hp i (mem_insert_of_mem hi)) hx with
       ⟨t, u, b, c, htus, htu, hbc, rfl, rfl⟩
@@ -44,11 +44,11 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
     have hiu : i ∉ u := fun hiu => his (htus ▸ mem_union_right _ hiu)
     obtain ⟨d, rfl⟩ | ⟨d, rfl⟩ : p i ∣ b ∨ p i ∣ c
     exact hpi.dvd_or_dvd ⟨a, by rw [← hbc, mul_comm]⟩
-    · rw [mul_assoc, mul_comm a, mul_right_inj' hpi.ne_zero] at hbc 
+    · rw [mul_assoc, mul_comm a, mul_right_inj' hpi.ne_zero] at hbc
       exact
         ⟨insert i t, u, d, c, by rw [insert_union, htus], disjoint_insert_left.2 ⟨hiu, htu⟩, by
           simp [hbc, prod_insert hit, mul_assoc, mul_comm, mul_left_comm]⟩
-    · rw [← mul_assoc, mul_right_comm b, mul_left_inj' hpi.ne_zero] at hbc 
+    · rw [← mul_assoc, mul_right_comm b, mul_left_inj' hpi.ne_zero] at hbc
       exact
         ⟨t, insert i u, b, d, by rw [union_insert, htus], disjoint_insert_right.2 ⟨hit, htu⟩, by
           simp [← hbc, prod_insert hiu, mul_assoc, mul_comm, mul_left_comm]⟩

327c3c0d

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Algebra.Associated
-import Mathbin.Algebra.BigOperators.Basic
+import Algebra.Associated
+import Algebra.BigOperators.Basic
 
 #align_import ring_theory.prime from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"

327c3c0d

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.prime
-! leanprover-community/mathlib commit 327c3c0d9232d80e250dc8f65e7835b82b266ea5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Associated
 import Mathbin.Algebra.BigOperators.Basic
 
+#align_import ring_theory.prime from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"
+
 /-!
 # Prime elements in rings

327c3c0d

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -28,6 +28,7 @@ open Finset
 
 open scoped BigOperators
 
+#print mul_eq_mul_prime_prod /-
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by
   a product over a subset of `s`  -/
@@ -55,7 +56,9 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
         ⟨t, insert i u, b, d, by rw [union_insert, htus], disjoint_insert_right.2 ⟨hit, htu⟩, by
           simp [← hbc, prod_insert hiu, mul_assoc, mul_comm, mul_left_comm]⟩
 #align mul_eq_mul_prime_prod mul_eq_mul_prime_prod
+-/
 
+#print mul_eq_mul_prime_pow /-
 /-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/
 theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y = a * p ^ n) :
@@ -66,6 +69,7 @@ theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y
     ⟨t, u, b, c, htus, htu, rfl, rfl, rfl⟩
   exact ⟨t.card, u.card, b, c, by rw [← card_disjoint_union htu, htus, card_range], by simp⟩
 #align mul_eq_mul_prime_pow mul_eq_mul_prime_pow
+-/
 
 end CancelCommMonoidWithZero
 
@@ -73,18 +77,22 @@ section CommRing
 
 variable {α : Type _} [CommRing α]
 
+#print Prime.neg /-
 theorem Prime.neg {p : α} (hp : Prime p) : Prime (-p) :=
   by
   obtain ⟨h1, h2, h3⟩ := hp
   exact ⟨neg_ne_zero.mpr h1, by rwa [IsUnit.neg_iff], by simpa [neg_dvd] using h3⟩
 #align prime.neg Prime.neg
+-/
 
+#print Prime.abs /-
 theorem Prime.abs [LinearOrder α] {p : α} (hp : Prime p) : Prime (abs p) :=
   by
   obtain h | h := abs_choice p <;> rw [h]
   · exact hp
   · exact hp.neg
 #align prime.abs Prime.abs
+-/
 
 end CommRing

327c3c0d

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -34,7 +34,7 @@ open scoped BigOperators
 theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Finset α} {p : α → R}
     (hp : ∀ i ∈ s, Prime (p i)) (hx : x * y = a * ∏ i in s, p i) :
     ∃ (t u : Finset α) (b c : R),
-      t ∪ u = s ∧ Disjoint t u ∧ a = b * c ∧ (x = b * ∏ i in t, p i) ∧ y = c * ∏ i in u, p i :=
+      t ∪ u = s ∧ Disjoint t u ∧ a = b * c ∧ x = b * ∏ i in t, p i ∧ y = c * ∏ i in u, p i :=
   by
   induction' s using Finset.induction with i s his ih generalizing x y a
   · exact ⟨∅, ∅, x, y, by simp [hx]⟩

327c3c0d

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -33,12 +33,12 @@ open scoped BigOperators
   a product over a subset of `s`  -/
 theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Finset α} {p : α → R}
     (hp : ∀ i ∈ s, Prime (p i)) (hx : x * y = a * ∏ i in s, p i) :
-    ∃ (t u : Finset α)(b c : R),
+    ∃ (t u : Finset α) (b c : R),
       t ∪ u = s ∧ Disjoint t u ∧ a = b * c ∧ (x = b * ∏ i in t, p i) ∧ y = c * ∏ i in u, p i :=
   by
   induction' s using Finset.induction with i s his ih generalizing x y a
   · exact ⟨∅, ∅, x, y, by simp [hx]⟩
-  · rw [prod_insert his, ← mul_assoc] at hx
+  · rw [prod_insert his, ← mul_assoc] at hx 
     have hpi : Prime (p i) := hp i (mem_insert_self _ _)
     rcases ih (fun i hi => hp i (mem_insert_of_mem hi)) hx with
       ⟨t, u, b, c, htus, htu, hbc, rfl, rfl⟩
@@ -46,11 +46,11 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
     have hiu : i ∉ u := fun hiu => his (htus ▸ mem_union_right _ hiu)
     obtain ⟨d, rfl⟩ | ⟨d, rfl⟩ : p i ∣ b ∨ p i ∣ c
     exact hpi.dvd_or_dvd ⟨a, by rw [← hbc, mul_comm]⟩
-    · rw [mul_assoc, mul_comm a, mul_right_inj' hpi.ne_zero] at hbc
+    · rw [mul_assoc, mul_comm a, mul_right_inj' hpi.ne_zero] at hbc 
       exact
         ⟨insert i t, u, d, c, by rw [insert_union, htus], disjoint_insert_left.2 ⟨hiu, htu⟩, by
           simp [hbc, prod_insert hit, mul_assoc, mul_comm, mul_left_comm]⟩
-    · rw [← mul_assoc, mul_right_comm b, mul_left_inj' hpi.ne_zero] at hbc
+    · rw [← mul_assoc, mul_right_comm b, mul_left_inj' hpi.ne_zero] at hbc 
       exact
         ⟨t, insert i u, b, d, by rw [union_insert, htus], disjoint_insert_right.2 ⟨hit, htu⟩, by
           simp [← hbc, prod_insert hiu, mul_assoc, mul_comm, mul_left_comm]⟩
@@ -59,7 +59,7 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
 /-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/
 theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y = a * p ^ n) :
-    ∃ (i j : ℕ)(b c : R), i + j = n ∧ a = b * c ∧ x = b * p ^ i ∧ y = c * p ^ j :=
+    ∃ (i j : ℕ) (b c : R), i + j = n ∧ a = b * c ∧ x = b * p ^ i ∧ y = c * p ^ j :=
   by
   rcases mul_eq_mul_prime_prod (fun _ _ => hp)
       (show x * y = a * (range n).Prod fun _ => p by simpa) with

327c3c0d

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ variable {R : Type _} [CancelCommMonoidWithZero R]
 
 open Finset
 
-open BigOperators
+open scoped BigOperators
 
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by

327c3c0d

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -28,9 +28,6 @@ open Finset
 
 open BigOperators
 
-/- warning: mul_eq_mul_prime_prod -> mul_eq_mul_prime_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mul_eq_mul_prime_prod mul_eq_mul_prime_prodₓ'. -/
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by
   a product over a subset of `s`  -/
@@ -59,9 +56,6 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
           simp [← hbc, prod_insert hiu, mul_assoc, mul_comm, mul_left_comm]⟩
 #align mul_eq_mul_prime_prod mul_eq_mul_prime_prod
 
-/- warning: mul_eq_mul_prime_pow -> mul_eq_mul_prime_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mul_eq_mul_prime_pow mul_eq_mul_prime_powₓ'. -/
 /-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/
 theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y = a * p ^ n) :
@@ -79,24 +73,12 @@ section CommRing
 
 variable {α : Type _} [CommRing α]
 
-/- warning: prime.neg -> Prime.neg is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) p))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) p))
-Case conversion may be inaccurate. Consider using '#align prime.neg Prime.negₓ'. -/
 theorem Prime.neg {p : α} (hp : Prime p) : Prime (-p) :=
   by
   obtain ⟨h1, h2, h3⟩ := hp
   exact ⟨neg_ne_zero.mpr h1, by rwa [IsUnit.neg_iff], by simpa [neg_dvd] using h3⟩
 #align prime.neg Prime.neg
 
-/- warning: prime.abs -> Prime.abs is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) p))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) p))
-Case conversion may be inaccurate. Consider using '#align prime.abs Prime.absₓ'. -/
 theorem Prime.abs [LinearOrder α] {p : α} (hp : Prime p) : Prime (abs p) :=
   by
   obtain h | h := abs_choice p <;> rw [h]

327c3c0d

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -29,10 +29,7 @@ open Finset
 open BigOperators
 
 /- warning: mul_eq_mul_prime_prod -> mul_eq_mul_prime_prod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {α : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} α] {x : R} {y : R} {a : R} {s : Finset.{u2} α} {p : α -> R}, (forall (i : α), (Membership.Mem.{u2, u2} α (Finset.{u2} α) (Finset.hasMem.{u2} α) i s) -> (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) (p i))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) x y) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) a (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) s (fun (i : α) => p i)))) -> (Exists.{succ u2} (Finset.{u2} α) (fun (t : Finset.{u2} α) => Exists.{succ u2} (Finset.{u2} α) (fun (u : Finset.{u2} α) => Exists.{succ u1} R (fun (b : R) => Exists.{succ u1} R (fun (c : R) => And (Eq.{succ u2} (Finset.{u2} α) (Union.union.{u2} (Finset.{u2} α) (Finset.hasUnion.{u2} α (fun (a : α) (b : α) => _inst_2 a b)) t u) s) (And (Disjoint.{u2} (Finset.{u2} α) (Finset.partialOrder.{u2} α) (Finset.orderBot.{u2} α) t u) (And (Eq.{succ u1} R a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b c)) (And (Eq.{succ u1} R x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) t (fun (i : α) => p i)))) (Eq.{succ u1} R y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) c (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) u (fun (i : α) => p i))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {α : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} α] {x : R} {y : R} {a : R} {s : Finset.{u2} α} {p : α -> R}, (forall (i : α), (Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) i s) -> (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) (p i))) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) x y) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) a (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) s (fun (i : α) => p i)))) -> (Exists.{succ u2} (Finset.{u2} α) (fun (t : Finset.{u2} α) => Exists.{succ u2} (Finset.{u2} α) (fun (u : Finset.{u2} α) => Exists.{succ u1} R (fun (b : R) => Exists.{succ u1} R (fun (c : R) => And (Eq.{succ u2} (Finset.{u2} α) (Union.union.{u2} (Finset.{u2} α) (Finset.instUnionFinset.{u2} α (fun (a : α) (b : α) => _inst_2 a b)) t u) s) (And (Disjoint.{u2} (Finset.{u2} α) (Finset.partialOrder.{u2} α) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u2} α) t u) (And (Eq.{succ u1} R a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b c)) (And (Eq.{succ u1} R x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) t (fun (i : α) => p i)))) (Eq.{succ u1} R y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) c (Finset.prod.{u1, u2} R α (CommMonoidWithZero.toCommMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)) u (fun (i : α) => p i))))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mul_eq_mul_prime_prod mul_eq_mul_prime_prodₓ'. -/
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by
@@ -63,10 +60,7 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
 #align mul_eq_mul_prime_prod mul_eq_mul_prime_prod
 
 /- warning: mul_eq_mul_prime_pow -> mul_eq_mul_prime_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R} {y : R} {a : R} {p : R} {n : Nat}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) p) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) x y) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p n))) -> (Exists.{1} Nat (fun (i : Nat) => Exists.{1} Nat (fun (j : Nat) => Exists.{succ u1} R (fun (b : R) => Exists.{succ u1} R (fun (c : R) => And (Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i j) n) (And (Eq.{succ u1} R a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b c)) (And (Eq.{succ u1} R x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p i))) (Eq.{succ u1} R y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) c (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p j))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CancelCommMonoidWithZero.{u1} R] {x : R} {y : R} {a : R} {p : R} {n : Nat}, (Prime.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1) p) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) x y) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) a (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p n))) -> (Exists.{1} Nat (fun (i : Nat) => Exists.{1} Nat (fun (j : Nat) => Exists.{succ u1} R (fun (b : R) => Exists.{succ u1} R (fun (c : R) => And (Eq.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i j) n) (And (Eq.{succ u1} R a (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b c)) (And (Eq.{succ u1} R x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) b (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p i))) (Eq.{succ u1} R y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1)))))) c (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R _inst_1))))) p j))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mul_eq_mul_prime_pow mul_eq_mul_prime_powₓ'. -/
 /-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/

327c3c0d

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -87,7 +87,7 @@ variable {α : Type _} [CommRing α]
 
 /- warning: prime.neg -> Prime.neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) p))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) p))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) p))
 Case conversion may be inaccurate. Consider using '#align prime.neg Prime.negₓ'. -/
@@ -99,7 +99,7 @@ theorem Prime.neg {p : α} (hp : Prime p) : Prime (-p) :=
 
 /- warning: prime.abs -> Prime.abs is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) p))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) p))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) p))
 Case conversion may be inaccurate. Consider using '#align prime.abs Prime.absₓ'. -/

327c3c0d

bump to nightly-2023-02-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

2097f8af

Diff

@@ -101,7 +101,7 @@ theorem Prime.neg {p : α} (hp : Prime p) : Prime (-p) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (CommRing.toRing.{u1} α _inst_1)))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) p))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) p))
+  forall {α : Type.{u1}} [_inst_1 : CommRing.{u1} α] [_inst_2 : LinearOrder.{u1} α] {p : α}, (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) p) -> (Prime.{u1} α (CommSemiring.toCommMonoidWithZero.{u1} α (CommRing.toCommSemiring.{u1} α _inst_1)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (CommRing.toRing.{u1} α _inst_1)) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) p))
 Case conversion may be inaccurate. Consider using '#align prime.abs Prime.absₓ'. -/
 theorem Prime.abs [LinearOrder α] {p : α} (hp : Prime p) : Prime (abs p) :=
   by

327c3c0d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

008205aa

chore: remove stream-of-conciousness syntax for obtain (#11045)

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

cd23c669

Diff

@@ -37,8 +37,7 @@ theorem mul_eq_mul_prime_prod {α : Type*} [DecidableEq α] {x y a : R} {s : Fin
       ⟨t, u, b, c, htus, htu, hbc, rfl, rfl⟩
     have hit : i ∉ t := fun hit ↦ his (htus ▸ mem_union_left _ hit)
     have hiu : i ∉ u := fun hiu ↦ his (htus ▸ mem_union_right _ hiu)
-    obtain ⟨d, rfl⟩ | ⟨d, rfl⟩ : p i ∣ b ∨ p i ∣ c
-    exact hpi.dvd_or_dvd ⟨a, by rw [← hbc, mul_comm]⟩
+    obtain ⟨d, rfl⟩ | ⟨d, rfl⟩ : p i ∣ b ∨ p i ∣ c := hpi.dvd_or_dvd ⟨a, by rw [← hbc, mul_comm]⟩
     · rw [mul_assoc, mul_comm a, mul_right_inj' hpi.ne_zero] at hbc
       exact ⟨insert i t, u, d, c, by rw [insert_union, htus], disjoint_insert_left.2 ⟨hiu, htu⟩, by
           simp [hbc, prod_insert hit, mul_assoc, mul_comm, mul_left_comm]⟩

008205aa

feat: (s ∩ t).card = s.card + t.card - (s ∪ t).card (#10224)

once coerced to an AddGroupWithOne. Also unify Finset.card_disjoint_union and Finset.card_union_eq

From LeanAPAP

80bf34f1

Diff

@@ -54,7 +54,7 @@ theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y
   rcases mul_eq_mul_prime_prod (fun _ _ ↦ hp)
     (show x * y = a * (range n).prod fun _ ↦ p by simpa) with
       ⟨t, u, b, c, htus, htu, rfl, rfl, rfl⟩
-  exact ⟨t.card, u.card, b, c, by rw [← card_disjoint_union htu, htus, card_range], by simp⟩
+  exact ⟨t.card, u.card, b, c, by rw [← card_union_of_disjoint htu, htus, card_range], by simp⟩
 #align mul_eq_mul_prime_pow mul_eq_mul_prime_pow
 
 end CancelCommMonoidWithZero

008205aa

chore: remove trailing space in backticks (#7617)

This will improve spaces in the mathlib4 docs.

9106dcf8

Diff

@@ -47,7 +47,7 @@ theorem mul_eq_mul_prime_prod {α : Type*} [DecidableEq α] {x y a : R} {s : Fin
           simp [← hbc, prod_insert hiu, mul_assoc, mul_comm, mul_left_comm]⟩
 #align mul_eq_mul_prime_prod mul_eq_mul_prime_prod
 
-/-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
+/-- If `x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/
 theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y = a * p ^ n) :
     ∃ (i j : ℕ) (b c : R), i + j = n ∧ a = b * c ∧ x = b * p ^ i ∧ y = c * p ^ j := by

008205aa

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

@@ -16,7 +16,7 @@ This file contains lemmas about prime elements of commutative rings.
 
 section CancelCommMonoidWithZero
 
-variable {R : Type _} [CancelCommMonoidWithZero R]
+variable {R : Type*} [CancelCommMonoidWithZero R]
 
 open Finset
 
@@ -25,7 +25,7 @@ open BigOperators
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by
   a product over a subset of `s`  -/
-theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Finset α} {p : α → R}
+theorem mul_eq_mul_prime_prod {α : Type*} [DecidableEq α] {x y a : R} {s : Finset α} {p : α → R}
     (hp : ∀ i ∈ s, Prime (p i)) (hx : x * y = a * ∏ i in s, p i) :
     ∃ (t u : Finset α) (b c : R),
       t ∪ u = s ∧ Disjoint t u ∧ a = b * c ∧ (x = b * ∏ i in t, p i) ∧ y = c * ∏ i in u, p i := by
@@ -61,7 +61,7 @@ end CancelCommMonoidWithZero
 
 section CommRing
 
-variable {α : Type _} [CommRing α]
+variable {α : Type*} [CommRing α]
 
 theorem Prime.neg {p : α} (hp : Prime p) : Prime (-p) := by
   obtain ⟨h1, h2, h3⟩ := hp

008205aa

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.prime
-! leanprover-community/mathlib commit 008205aa645b3f194c1da47025c5f110c8406eab
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Associated
 import Mathlib.Algebra.BigOperators.Basic
 
+#align_import ring_theory.prime from "leanprover-community/mathlib"@"008205aa645b3f194c1da47025c5f110c8406eab"
+
 /-!
 # Prime elements in rings
 This file contains lemmas about prime elements of commutative rings.

008205aa

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -30,7 +30,7 @@ open BigOperators
   a product over a subset of `s`  -/
 theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Finset α} {p : α → R}
     (hp : ∀ i ∈ s, Prime (p i)) (hx : x * y = a * ∏ i in s, p i) :
-    ∃ (t u : Finset α)(b c : R),
+    ∃ (t u : Finset α) (b c : R),
       t ∪ u = s ∧ Disjoint t u ∧ a = b * c ∧ (x = b * ∏ i in t, p i) ∧ y = c * ∏ i in u, p i := by
   induction' s using Finset.induction with i s his ih generalizing x y a
   · exact ⟨∅, ∅, x, y, by simp [hx]⟩
@@ -53,7 +53,7 @@ theorem mul_eq_mul_prime_prod {α : Type _} [DecidableEq α] {x y a : R} {s : Fi
 /-- If ` x * y = a * p ^ n` where `p` is prime, then `x` and `y` can both be written
   as the product of a power of `p` and a divisor of `a`. -/
 theorem mul_eq_mul_prime_pow {x y a p : R} {n : ℕ} (hp : Prime p) (hx : x * y = a * p ^ n) :
-    ∃ (i j : ℕ)(b c : R), i + j = n ∧ a = b * c ∧ x = b * p ^ i ∧ y = c * p ^ j := by
+    ∃ (i j : ℕ) (b c : R), i + j = n ∧ a = b * c ∧ x = b * p ^ i ∧ y = c * p ^ j := by
   rcases mul_eq_mul_prime_prod (fun _ _ ↦ hp)
     (show x * y = a * (range n).prod fun _ ↦ p by simpa) with
       ⟨t, u, b, c, htus, htu, rfl, rfl, rfl⟩

008205aa

chore: scoped BigOperators notation (#1952)

e707fa67

Diff

@@ -23,8 +23,7 @@ variable {R : Type _} [CancelCommMonoidWithZero R]
 
 open Finset
 
--- Porting note: commented out the next line
--- open BigOperators
+open BigOperators
 
 /-- If `x * y = a * ∏ i in s, p i` where `p i` is always prime, then
   `x` and `y` can both be written as a divisor of `a` multiplied by

008205aa

feat port: RingTheory.Prime (#1646)

7092d7ca

`ring_theory.prime` ⟷ `Mathlib.RingTheory.Prime`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 191

ring_theory.prime ⟷ Mathlib.RingTheory.Prime

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 191

`ring_theory.prime` ⟷ `Mathlib.RingTheory.Prime`