ring_theory.coprime.basic | 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

a95b16cb

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

448144f7

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -68,7 +68,7 @@ theorem isCoprime_self : IsCoprime x x ↔ IsUnit x :=
 #print isCoprime_zero_left /-
 theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
   ⟨fun ⟨a, b, H⟩ =>
-    isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H , fun H =>
+    isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H, fun H =>
     let ⟨b, hb⟩ := isUnit_iff_exists_inv'.1 H
     ⟨1, b, by rwa [one_mul, zero_add]⟩⟩
 #align is_coprime_zero_left isCoprime_zero_left
@@ -164,7 +164,7 @@ theorem IsCoprime.of_mul_left_left (H : IsCoprime (x * y) z) : IsCoprime x z :=
 
 #print IsCoprime.of_mul_left_right /-
 theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z := by
-  rw [mul_comm] at H ; exact H.of_mul_left_left
+  rw [mul_comm] at H; exact H.of_mul_left_left
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
 -/
 
@@ -176,7 +176,7 @@ theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y :=
 
 #print IsCoprime.of_mul_right_right /-
 theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z := by
-  rw [mul_comm] at H ; exact H.of_mul_right_left
+  rw [mul_comm] at H; exact H.of_mul_right_left
 #align is_coprime.of_mul_right_right IsCoprime.of_mul_right_right
 -/
 
@@ -241,7 +241,7 @@ theorem IsCoprime.of_add_mul_left_left (h : IsCoprime (x + y * z) y) : IsCoprime
 
 #print IsCoprime.of_add_mul_right_left /-
 theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y := by
-  rw [mul_comm] at h ; exact h.of_add_mul_left_left
+  rw [mul_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
 -/
 
@@ -253,31 +253,31 @@ theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprim
 
 #print IsCoprime.of_add_mul_right_right /-
 theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y := by
-  rw [mul_comm] at h ; exact h.of_add_mul_left_right
+  rw [mul_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_right
 -/
 
 #print IsCoprime.of_mul_add_left_left /-
 theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y := by
-  rw [add_comm] at h ; exact h.of_add_mul_left_left
+  rw [add_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_left
 -/
 
 #print IsCoprime.of_mul_add_right_left /-
 theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y := by
-  rw [add_comm] at h ; exact h.of_add_mul_right_left
+  rw [add_comm] at h; exact h.of_add_mul_right_left
 #align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_left
 -/
 
 #print IsCoprime.of_mul_add_left_right /-
 theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y := by
-  rw [add_comm] at h ; exact h.of_add_mul_left_right
+  rw [add_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_right
 -/
 
 #print IsCoprime.of_mul_add_right_right /-
 theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y := by
-  rw [add_comm] at h ; exact h.of_add_mul_right_right
+  rw [add_comm] at h; exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
 -/

448144f7

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 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Ken Lee, Chris Hughes
 -/
-import Mathbin.Tactic.Ring
-import Mathbin.GroupTheory.GroupAction.Units
+import Tactic.Ring
+import GroupTheory.GroupAction.Units
 
 #align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"

448144f7

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -149,9 +149,9 @@ theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x
   rw [← mul_one z, ← h, mul_add]
   apply dvd_add
   · rw [mul_comm z, mul_assoc]
-    exact (mul_dvd_mul_left _ H2).mul_left _
+    exact (mul_dvd_mul_left _ H2).hMul_left _
   · rw [mul_comm b, ← mul_assoc]
-    exact (mul_dvd_mul_right H1 _).mul_right _
+    exact (mul_dvd_mul_right H1 _).hMul_right _
 #align is_coprime.mul_dvd IsCoprime.mul_dvd
 -/
 
@@ -182,7 +182,7 @@ theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z :
 
 #print IsCoprime.mul_left_iff /-
 theorem IsCoprime.mul_left_iff : IsCoprime (x * y) z ↔ IsCoprime x z ∧ IsCoprime y z :=
-  ⟨fun H => ⟨H.of_mul_left_left, H.of_mul_left_right⟩, fun ⟨H1, H2⟩ => H1.mul_left H2⟩
+  ⟨fun H => ⟨H.of_mul_left_left, H.of_mul_left_right⟩, fun ⟨H1, H2⟩ => H1.hMul_left H2⟩
 #align is_coprime.mul_left_iff IsCoprime.mul_left_iff
 -/

448144f7

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -459,7 +459,7 @@ theorem mul_add_right_right_iff {x y z : R} : IsCoprime x (z * x + y) ↔ IsCopr
 theorem neg_left {x y : R} (h : IsCoprime x y) : IsCoprime (-x) y :=
   by
   obtain ⟨a, b, h⟩ := h
-  use -a, b
+  use-a, b
   rwa [neg_mul_neg]
 #align is_coprime.neg_left IsCoprime.neg_left
 -/

448144f7

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 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Ken Lee, Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.coprime.basic
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Tactic.Ring
 import Mathbin.GroupTheory.GroupAction.Units
 
+#align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
 /-!
 # Coprime elements of a ring

448144f7

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -68,25 +68,33 @@ theorem isCoprime_self : IsCoprime x x ↔ IsUnit x :=
 #align is_coprime_self isCoprime_self
 -/
 
+#print isCoprime_zero_left /-
 theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
   ⟨fun ⟨a, b, H⟩ =>
     isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H , fun H =>
     let ⟨b, hb⟩ := isUnit_iff_exists_inv'.1 H
     ⟨1, b, by rwa [one_mul, zero_add]⟩⟩
 #align is_coprime_zero_left isCoprime_zero_left
+-/
 
+#print isCoprime_zero_right /-
 theorem isCoprime_zero_right : IsCoprime x 0 ↔ IsUnit x :=
   isCoprime_comm.trans isCoprime_zero_left
 #align is_coprime_zero_right isCoprime_zero_right
+-/
 
+#print not_isCoprime_zero_zero /-
 theorem not_isCoprime_zero_zero [Nontrivial R] : ¬IsCoprime (0 : R) 0 :=
   mt isCoprime_zero_right.mp not_isUnit_zero
 #align not_coprime_zero_zero not_isCoprime_zero_zero
+-/
 
+#print IsCoprime.ne_zero /-
 /-- If a 2-vector `p` satisfies `is_coprime (p 0) (p 1)`, then `p ≠ 0`. -/
 theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 := by
   rintro rfl; exact not_isCoprime_zero_zero h
 #align is_coprime.ne_zero IsCoprime.ne_zero
+-/
 
 #print isCoprime_one_left /-
 theorem isCoprime_one_left : IsCoprime 1 x :=
@@ -100,20 +108,25 @@ theorem isCoprime_one_right : IsCoprime x 1 :=
 #align is_coprime_one_right isCoprime_one_right
 -/
 
+#print IsCoprime.dvd_of_dvd_mul_right /-
 theorem IsCoprime.dvd_of_dvd_mul_right (H1 : IsCoprime x z) (H2 : x ∣ y * z) : x ∣ y :=
   by
   let ⟨a, b, H⟩ := H1
   rw [← mul_one y, ← H, mul_add, ← mul_assoc, mul_left_comm]
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_right IsCoprime.dvd_of_dvd_mul_right
+-/
 
+#print IsCoprime.dvd_of_dvd_mul_left /-
 theorem IsCoprime.dvd_of_dvd_mul_left (H1 : IsCoprime x y) (H2 : x ∣ y * z) : x ∣ z :=
   by
   let ⟨a, b, H⟩ := H1
   rw [← one_mul z, ← H, add_mul, mul_right_comm, mul_assoc b]
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_left IsCoprime.dvd_of_dvd_mul_left
+-/
 
+#print IsCoprime.mul_left /-
 theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime (x * y) z :=
   let ⟨a, b, h1⟩ := H1
   let ⟨c, d, h2⟩ := H2
@@ -124,11 +137,15 @@ theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime
         by ring
       _ = 1 := by rw [h1, h2, mul_one]⟩
 #align is_coprime.mul_left IsCoprime.mul_left
+-/
 
+#print IsCoprime.mul_right /-
 theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by
   rw [isCoprime_comm] at H1 H2 ⊢; exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
+-/
 
+#print IsCoprime.mul_dvd /-
 theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x * y ∣ z :=
   by
   obtain ⟨a, b, h⟩ := H
@@ -139,31 +156,44 @@ theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x
   · rw [mul_comm b, ← mul_assoc]
     exact (mul_dvd_mul_right H1 _).mul_right _
 #align is_coprime.mul_dvd IsCoprime.mul_dvd
+-/
 
+#print IsCoprime.of_mul_left_left /-
 theorem IsCoprime.of_mul_left_left (H : IsCoprime (x * y) z) : IsCoprime x z :=
   let ⟨a, b, h⟩ := H
   ⟨a * y, b, by rwa [mul_right_comm, mul_assoc]⟩
 #align is_coprime.of_mul_left_left IsCoprime.of_mul_left_left
+-/
 
+#print IsCoprime.of_mul_left_right /-
 theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z := by
   rw [mul_comm] at H ; exact H.of_mul_left_left
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
+-/
 
+#print IsCoprime.of_mul_right_left /-
 theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y := by
   rw [isCoprime_comm] at H ⊢; exact H.of_mul_left_left
 #align is_coprime.of_mul_right_left IsCoprime.of_mul_right_left
+-/
 
+#print IsCoprime.of_mul_right_right /-
 theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z := by
   rw [mul_comm] at H ; exact H.of_mul_right_left
 #align is_coprime.of_mul_right_right IsCoprime.of_mul_right_right
+-/
 
+#print IsCoprime.mul_left_iff /-
 theorem IsCoprime.mul_left_iff : IsCoprime (x * y) z ↔ IsCoprime x z ∧ IsCoprime y z :=
   ⟨fun H => ⟨H.of_mul_left_left, H.of_mul_left_right⟩, fun ⟨H1, H2⟩ => H1.mul_left H2⟩
 #align is_coprime.mul_left_iff IsCoprime.mul_left_iff
+-/
 
+#print IsCoprime.mul_right_iff /-
 theorem IsCoprime.mul_right_iff : IsCoprime x (y * z) ↔ IsCoprime x y ∧ IsCoprime x z := by
   rw [isCoprime_comm, IsCoprime.mul_left_iff, isCoprime_comm, @isCoprime_comm _ _ z]
 #align is_coprime.mul_right_iff IsCoprime.mul_right_iff
+-/
 
 #print IsCoprime.of_isCoprime_of_dvd_left /-
 theorem IsCoprime.of_isCoprime_of_dvd_left (h : IsCoprime y z) (hdvd : x ∣ y) : IsCoprime x z :=
@@ -193,48 +223,66 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
 #align is_coprime.is_unit_of_dvd' IsCoprime.isUnit_of_dvd'
 -/
 
+#print IsCoprime.map /-
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=
   let ⟨a, b, h⟩ := H
   ⟨f a, f b, by rw [← f.map_mul, ← f.map_mul, ← f.map_add, h, f.map_one]⟩
 #align is_coprime.map IsCoprime.map
+-/
 
 variable {x y z}
 
+#print IsCoprime.of_add_mul_left_left /-
 theorem IsCoprime.of_add_mul_left_left (h : IsCoprime (x + y * z) y) : IsCoprime x y :=
   let ⟨a, b, H⟩ := h
   ⟨a, a * z + b, by
     simpa only [add_mul, mul_add, add_assoc, add_comm, add_left_comm, mul_assoc, mul_comm,
       mul_left_comm] using H⟩
 #align is_coprime.of_add_mul_left_left IsCoprime.of_add_mul_left_left
+-/
 
+#print IsCoprime.of_add_mul_right_left /-
 theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y := by
   rw [mul_comm] at h ; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
+-/
 
+#print IsCoprime.of_add_mul_left_right /-
 theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y := by
   rw [isCoprime_comm] at h ⊢; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_right
+-/
 
+#print IsCoprime.of_add_mul_right_right /-
 theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y := by
   rw [mul_comm] at h ; exact h.of_add_mul_left_right
 #align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_right
+-/
 
+#print IsCoprime.of_mul_add_left_left /-
 theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y := by
   rw [add_comm] at h ; exact h.of_add_mul_left_left
 #align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_left
+-/
 
+#print IsCoprime.of_mul_add_right_left /-
 theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y := by
   rw [add_comm] at h ; exact h.of_add_mul_right_left
 #align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_left
+-/
 
+#print IsCoprime.of_mul_add_left_right /-
 theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y := by
   rw [add_comm] at h ; exact h.of_add_mul_left_right
 #align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_right
+-/
 
+#print IsCoprime.of_mul_add_right_right /-
 theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y := by
   rw [add_comm] at h ; exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
+-/
 
 end CommSemiring
 
@@ -243,18 +291,24 @@ section ScalarTower
 variable {R G : Type _} [CommSemiring R] [Group G] [MulAction G R] [SMulCommClass G R R]
   [IsScalarTower G R R] (x : G) (y z : R)
 
+#print isCoprime_group_smul_left /-
 theorem isCoprime_group_smul_left : IsCoprime (x • y) z ↔ IsCoprime y z :=
   ⟨fun ⟨a, b, h⟩ => ⟨x • a, b, by rwa [smul_mul_assoc, ← mul_smul_comm]⟩, fun ⟨a, b, h⟩ =>
     ⟨x⁻¹ • a, b, by rwa [smul_mul_smul, inv_mul_self, one_smul]⟩⟩
 #align is_coprime_group_smul_left isCoprime_group_smul_left
+-/
 
+#print isCoprime_group_smul_right /-
 theorem isCoprime_group_smul_right : IsCoprime y (x • z) ↔ IsCoprime y z :=
   isCoprime_comm.trans <| (isCoprime_group_smul_left x z y).trans isCoprime_comm
 #align is_coprime_group_smul_right isCoprime_group_smul_right
+-/
 
+#print isCoprime_group_smul /-
 theorem isCoprime_group_smul : IsCoprime (x • y) (x • z) ↔ IsCoprime y z :=
   (isCoprime_group_smul_left x y (x • z)).trans (isCoprime_group_smul_right x y z)
 #align is_coprime_group_smul isCoprime_group_smul
+-/
 
 end ScalarTower
 
@@ -262,31 +316,43 @@ section CommSemiringUnit
 
 variable {R : Type _} [CommSemiring R] {x : R} (hu : IsUnit x) (y z : R)
 
+#print isCoprime_mul_unit_left_left /-
 theorem isCoprime_mul_unit_left_left : IsCoprime (x * y) z ↔ IsCoprime y z :=
   let ⟨u, hu⟩ := hu
   hu ▸ isCoprime_group_smul_left u y z
 #align is_coprime_mul_unit_left_left isCoprime_mul_unit_left_left
+-/
 
+#print isCoprime_mul_unit_left_right /-
 theorem isCoprime_mul_unit_left_right : IsCoprime y (x * z) ↔ IsCoprime y z :=
   let ⟨u, hu⟩ := hu
   hu ▸ isCoprime_group_smul_right u y z
 #align is_coprime_mul_unit_left_right isCoprime_mul_unit_left_right
+-/
 
+#print isCoprime_mul_unit_left /-
 theorem isCoprime_mul_unit_left : IsCoprime (x * y) (x * z) ↔ IsCoprime y z :=
   (isCoprime_mul_unit_left_left hu y (x * z)).trans (isCoprime_mul_unit_left_right hu y z)
 #align is_coprime_mul_unit_left isCoprime_mul_unit_left
+-/
 
+#print isCoprime_mul_unit_right_left /-
 theorem isCoprime_mul_unit_right_left : IsCoprime (y * x) z ↔ IsCoprime y z :=
   mul_comm x y ▸ isCoprime_mul_unit_left_left hu y z
 #align is_coprime_mul_unit_right_left isCoprime_mul_unit_right_left
+-/
 
+#print isCoprime_mul_unit_right_right /-
 theorem isCoprime_mul_unit_right_right : IsCoprime y (z * x) ↔ IsCoprime y z :=
   mul_comm x z ▸ isCoprime_mul_unit_left_right hu y z
 #align is_coprime_mul_unit_right_right isCoprime_mul_unit_right_right
+-/
 
+#print isCoprime_mul_unit_right /-
 theorem isCoprime_mul_unit_right : IsCoprime (y * x) (z * x) ↔ IsCoprime y z :=
   (isCoprime_mul_unit_right_left hu y (z * x)).trans (isCoprime_mul_unit_right_right hu y z)
 #align is_coprime_mul_unit_right isCoprime_mul_unit_right
+-/
 
 end CommSemiringUnit
 
@@ -296,99 +362,144 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
+#print IsCoprime.add_mul_left_left /-
 theorem add_mul_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + y * z) y :=
   @of_add_mul_left_left R _ _ _ (-z) <| by simpa only [mul_neg, add_neg_cancel_right] using h
 #align is_coprime.add_mul_left_left IsCoprime.add_mul_left_left
+-/
 
+#print IsCoprime.add_mul_right_left /-
 theorem add_mul_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + z * y) y := by
   rw [mul_comm]; exact h.add_mul_left_left z
 #align is_coprime.add_mul_right_left IsCoprime.add_mul_right_left
+-/
 
+#print IsCoprime.add_mul_left_right /-
 theorem add_mul_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + x * z) := by
   rw [isCoprime_comm]; exact h.symm.add_mul_left_left z
 #align is_coprime.add_mul_left_right IsCoprime.add_mul_left_right
+-/
 
+#print IsCoprime.add_mul_right_right /-
 theorem add_mul_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + z * x) := by
   rw [isCoprime_comm]; exact h.symm.add_mul_right_left z
 #align is_coprime.add_mul_right_right IsCoprime.add_mul_right_right
+-/
 
+#print IsCoprime.mul_add_left_left /-
 theorem mul_add_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (y * z + x) y := by
   rw [add_comm]; exact h.add_mul_left_left z
 #align is_coprime.mul_add_left_left IsCoprime.mul_add_left_left
+-/
 
+#print IsCoprime.mul_add_right_left /-
 theorem mul_add_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (z * y + x) y := by
   rw [add_comm]; exact h.add_mul_right_left z
 #align is_coprime.mul_add_right_left IsCoprime.mul_add_right_left
+-/
 
+#print IsCoprime.mul_add_left_right /-
 theorem mul_add_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (x * z + y) := by
   rw [add_comm]; exact h.add_mul_left_right z
 #align is_coprime.mul_add_left_right IsCoprime.mul_add_left_right
+-/
 
+#print IsCoprime.mul_add_right_right /-
 theorem mul_add_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (z * x + y) := by
   rw [add_comm]; exact h.add_mul_right_right z
 #align is_coprime.mul_add_right_right IsCoprime.mul_add_right_right
+-/
 
+#print IsCoprime.add_mul_left_left_iff /-
 theorem add_mul_left_left_iff {x y z : R} : IsCoprime (x + y * z) y ↔ IsCoprime x y :=
   ⟨of_add_mul_left_left, fun h => h.add_mul_left_left z⟩
 #align is_coprime.add_mul_left_left_iff IsCoprime.add_mul_left_left_iff
+-/
 
+#print IsCoprime.add_mul_right_left_iff /-
 theorem add_mul_right_left_iff {x y z : R} : IsCoprime (x + z * y) y ↔ IsCoprime x y :=
   ⟨of_add_mul_right_left, fun h => h.add_mul_right_left z⟩
 #align is_coprime.add_mul_right_left_iff IsCoprime.add_mul_right_left_iff
+-/
 
+#print IsCoprime.add_mul_left_right_iff /-
 theorem add_mul_left_right_iff {x y z : R} : IsCoprime x (y + x * z) ↔ IsCoprime x y :=
   ⟨of_add_mul_left_right, fun h => h.add_mul_left_right z⟩
 #align is_coprime.add_mul_left_right_iff IsCoprime.add_mul_left_right_iff
+-/
 
+#print IsCoprime.add_mul_right_right_iff /-
 theorem add_mul_right_right_iff {x y z : R} : IsCoprime x (y + z * x) ↔ IsCoprime x y :=
   ⟨of_add_mul_right_right, fun h => h.add_mul_right_right z⟩
 #align is_coprime.add_mul_right_right_iff IsCoprime.add_mul_right_right_iff
+-/
 
+#print IsCoprime.mul_add_left_left_iff /-
 theorem mul_add_left_left_iff {x y z : R} : IsCoprime (y * z + x) y ↔ IsCoprime x y :=
   ⟨of_mul_add_left_left, fun h => h.mul_add_left_left z⟩
 #align is_coprime.mul_add_left_left_iff IsCoprime.mul_add_left_left_iff
+-/
 
+#print IsCoprime.mul_add_right_left_iff /-
 theorem mul_add_right_left_iff {x y z : R} : IsCoprime (z * y + x) y ↔ IsCoprime x y :=
   ⟨of_mul_add_right_left, fun h => h.mul_add_right_left z⟩
 #align is_coprime.mul_add_right_left_iff IsCoprime.mul_add_right_left_iff
+-/
 
+#print IsCoprime.mul_add_left_right_iff /-
 theorem mul_add_left_right_iff {x y z : R} : IsCoprime x (x * z + y) ↔ IsCoprime x y :=
   ⟨of_mul_add_left_right, fun h => h.mul_add_left_right z⟩
 #align is_coprime.mul_add_left_right_iff IsCoprime.mul_add_left_right_iff
+-/
 
+#print IsCoprime.mul_add_right_right_iff /-
 theorem mul_add_right_right_iff {x y z : R} : IsCoprime x (z * x + y) ↔ IsCoprime x y :=
   ⟨of_mul_add_right_right, fun h => h.mul_add_right_right z⟩
 #align is_coprime.mul_add_right_right_iff IsCoprime.mul_add_right_right_iff
+-/
 
+#print IsCoprime.neg_left /-
 theorem neg_left {x y : R} (h : IsCoprime x y) : IsCoprime (-x) y :=
   by
   obtain ⟨a, b, h⟩ := h
   use -a, b
   rwa [neg_mul_neg]
 #align is_coprime.neg_left IsCoprime.neg_left
+-/
 
+#print IsCoprime.neg_left_iff /-
 theorem neg_left_iff (x y : R) : IsCoprime (-x) y ↔ IsCoprime x y :=
   ⟨fun h => neg_neg x ▸ h.neg_left, neg_left⟩
 #align is_coprime.neg_left_iff IsCoprime.neg_left_iff
+-/
 
+#print IsCoprime.neg_right /-
 theorem neg_right {x y : R} (h : IsCoprime x y) : IsCoprime x (-y) :=
   h.symm.neg_left.symm
 #align is_coprime.neg_right IsCoprime.neg_right
+-/
 
+#print IsCoprime.neg_right_iff /-
 theorem neg_right_iff (x y : R) : IsCoprime x (-y) ↔ IsCoprime x y :=
   ⟨fun h => neg_neg y ▸ h.neg_right, neg_right⟩
 #align is_coprime.neg_right_iff IsCoprime.neg_right_iff
+-/
 
+#print IsCoprime.neg_neg /-
 theorem neg_neg {x y : R} (h : IsCoprime x y) : IsCoprime (-x) (-y) :=
   h.neg_left.neg_right
 #align is_coprime.neg_neg IsCoprime.neg_neg
+-/
 
+#print IsCoprime.neg_neg_iff /-
 theorem neg_neg_iff (x y : R) : IsCoprime (-x) (-y) ↔ IsCoprime x y :=
   (neg_left_iff _ _).trans (neg_right_iff _ _)
 #align is_coprime.neg_neg_iff IsCoprime.neg_neg_iff
+-/
 
 end CommRing
 
+#print IsCoprime.sq_add_sq_ne_zero /-
 theorem sq_add_sq_ne_zero {R : Type _} [LinearOrderedCommRing R] {a b : R} (h : IsCoprime a b) :
     a ^ 2 + b ^ 2 ≠ 0 := by
   intro h'
@@ -397,6 +508,7 @@ theorem sq_add_sq_ne_zero {R : Type _} [LinearOrderedCommRing R] {a b : R} (h :
   obtain rfl := pow_eq_zero hb
   exact not_isCoprime_zero_zero h
 #align is_coprime.sq_add_sq_ne_zero IsCoprime.sq_add_sq_ne_zero
+-/
 
 end IsCoprime

448144f7

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -122,8 +122,7 @@ theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime
       a * c * (x * y) + (a * x * d + b * c * y + b * d * z) * z =
           (a * x + b * z) * (c * y + d * z) :=
         by ring
-      _ = 1 := by rw [h1, h2, mul_one]
-      ⟩
+      _ = 1 := by rw [h1, h2, mul_one]⟩
 #align is_coprime.mul_left IsCoprime.mul_left
 
 theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by

448144f7

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -70,7 +70,7 @@ theorem isCoprime_self : IsCoprime x x ↔ IsUnit x :=
 
 theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
   ⟨fun ⟨a, b, H⟩ =>
-    isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H, fun H =>
+    isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H , fun H =>
     let ⟨b, hb⟩ := isUnit_iff_exists_inv'.1 H
     ⟨1, b, by rwa [one_mul, zero_add]⟩⟩
 #align is_coprime_zero_left isCoprime_zero_left
@@ -127,7 +127,7 @@ theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime
 #align is_coprime.mul_left IsCoprime.mul_left
 
 theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by
-  rw [isCoprime_comm] at H1 H2⊢; exact H1.mul_left H2
+  rw [isCoprime_comm] at H1 H2 ⊢; exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
 theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x * y ∣ z :=
@@ -147,15 +147,15 @@ theorem IsCoprime.of_mul_left_left (H : IsCoprime (x * y) z) : IsCoprime x z :=
 #align is_coprime.of_mul_left_left IsCoprime.of_mul_left_left
 
 theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z := by
-  rw [mul_comm] at H; exact H.of_mul_left_left
+  rw [mul_comm] at H ; exact H.of_mul_left_left
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
 
 theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y := by
-  rw [isCoprime_comm] at H⊢; exact H.of_mul_left_left
+  rw [isCoprime_comm] at H ⊢; exact H.of_mul_left_left
 #align is_coprime.of_mul_right_left IsCoprime.of_mul_right_left
 
 theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z := by
-  rw [mul_comm] at H; exact H.of_mul_right_left
+  rw [mul_comm] at H ; exact H.of_mul_right_left
 #align is_coprime.of_mul_right_right IsCoprime.of_mul_right_right
 
 theorem IsCoprime.mul_left_iff : IsCoprime (x * y) z ↔ IsCoprime x z ∧ IsCoprime y z :=
@@ -210,31 +210,31 @@ theorem IsCoprime.of_add_mul_left_left (h : IsCoprime (x + y * z) y) : IsCoprime
 #align is_coprime.of_add_mul_left_left IsCoprime.of_add_mul_left_left
 
 theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y := by
-  rw [mul_comm] at h; exact h.of_add_mul_left_left
+  rw [mul_comm] at h ; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
 
 theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y := by
-  rw [isCoprime_comm] at h⊢; exact h.of_add_mul_left_left
+  rw [isCoprime_comm] at h ⊢; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_right
 
 theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y := by
-  rw [mul_comm] at h; exact h.of_add_mul_left_right
+  rw [mul_comm] at h ; exact h.of_add_mul_left_right
 #align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_right
 
 theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y := by
-  rw [add_comm] at h; exact h.of_add_mul_left_left
+  rw [add_comm] at h ; exact h.of_add_mul_left_left
 #align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_left
 
 theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y := by
-  rw [add_comm] at h; exact h.of_add_mul_right_left
+  rw [add_comm] at h ; exact h.of_add_mul_right_left
 #align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_left
 
 theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y := by
-  rw [add_comm] at h; exact h.of_add_mul_left_right
+  rw [add_comm] at h ; exact h.of_add_mul_left_right
 #align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_right
 
 theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y := by
-  rw [add_comm] at h; exact h.of_add_mul_right_right
+  rw [add_comm] at h ; exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
 
 end CommSemiring

448144f7

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ See also `ring_theory.coprime.lemmas` for further development of coprime element
 -/
 
 
-open Classical
+open scoped Classical
 
 universe u v

448144f7

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -68,12 +68,6 @@ theorem isCoprime_self : IsCoprime x x ↔ IsUnit x :=
 #align is_coprime_self isCoprime_self
 -/
 
-/- warning: is_coprime_zero_left -> isCoprime_zero_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R}, Iff (IsCoprime.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) x) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R}, Iff (IsCoprime.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))) x) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) x)
-Case conversion may be inaccurate. Consider using '#align is_coprime_zero_left isCoprime_zero_leftₓ'. -/
 theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
   ⟨fun ⟨a, b, H⟩ =>
     isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H, fun H =>
@@ -81,32 +75,14 @@ theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
     ⟨1, b, by rwa [one_mul, zero_add]⟩⟩
 #align is_coprime_zero_left isCoprime_zero_left
 
-/- warning: is_coprime_zero_right -> isCoprime_zero_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R}, Iff (IsCoprime.{u1} R _inst_1 x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))))) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R}, Iff (IsCoprime.{u1} R _inst_1 x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) x)
-Case conversion may be inaccurate. Consider using '#align is_coprime_zero_right isCoprime_zero_rightₓ'. -/
 theorem isCoprime_zero_right : IsCoprime x 0 ↔ IsUnit x :=
   isCoprime_comm.trans isCoprime_zero_left
 #align is_coprime_zero_right isCoprime_zero_right
 
-/- warning: not_coprime_zero_zero -> not_isCoprime_zero_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (IsCoprime.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R], Not (IsCoprime.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align not_coprime_zero_zero not_isCoprime_zero_zeroₓ'. -/
 theorem not_isCoprime_zero_zero [Nontrivial R] : ¬IsCoprime (0 : R) 0 :=
   mt isCoprime_zero_right.mp not_isUnit_zero
 #align not_coprime_zero_zero not_isCoprime_zero_zero
 
-/- warning: is_coprime.ne_zero -> IsCoprime.ne_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_coprime.ne_zero IsCoprime.ne_zeroₓ'. -/
 /-- If a 2-vector `p` satisfies `is_coprime (p 0) (p 1)`, then `p ≠ 0`. -/
 theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 := by
   rintro rfl; exact not_isCoprime_zero_zero h
@@ -124,12 +100,6 @@ theorem isCoprime_one_right : IsCoprime x 1 :=
 #align is_coprime_one_right isCoprime_one_right
 -/
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.dvd_of_dvd_mul_right IsCoprime.dvd_of_dvd_mul_rightₓ'. -/
 theorem IsCoprime.dvd_of_dvd_mul_right (H1 : IsCoprime x z) (H2 : x ∣ y * z) : x ∣ y :=
   by
   let ⟨a, b, H⟩ := H1
@@ -137,12 +107,6 @@ theorem IsCoprime.dvd_of_dvd_mul_right (H1 : IsCoprime x z) (H2 : x ∣ y * z) :
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_right IsCoprime.dvd_of_dvd_mul_right
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.dvd_of_dvd_mul_left IsCoprime.dvd_of_dvd_mul_leftₓ'. -/
 theorem IsCoprime.dvd_of_dvd_mul_left (H1 : IsCoprime x y) (H2 : x ∣ y * z) : x ∣ z :=
   by
   let ⟨a, b, H⟩ := H1
@@ -150,12 +114,6 @@ theorem IsCoprime.dvd_of_dvd_mul_left (H1 : IsCoprime x y) (H2 : x ∣ y * z) :
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_left IsCoprime.dvd_of_dvd_mul_left
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.mul_left IsCoprime.mul_leftₓ'. -/
 theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime (x * y) z :=
   let ⟨a, b, h1⟩ := H1
   let ⟨c, d, h2⟩ := H2
@@ -168,22 +126,10 @@ theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime
       ⟩
 #align is_coprime.mul_left IsCoprime.mul_left
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.mul_right IsCoprime.mul_rightₓ'. -/
 theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by
   rw [isCoprime_comm] at H1 H2⊢; exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.mul_dvd IsCoprime.mul_dvdₓ'. -/
 theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x * y ∣ z :=
   by
   obtain ⟨a, b, h⟩ := H
@@ -195,63 +141,27 @@ theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x
     exact (mul_dvd_mul_right H1 _).mul_right _
 #align is_coprime.mul_dvd IsCoprime.mul_dvd
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_left_left IsCoprime.of_mul_left_leftₓ'. -/
 theorem IsCoprime.of_mul_left_left (H : IsCoprime (x * y) z) : IsCoprime x z :=
   let ⟨a, b, h⟩ := H
   ⟨a * y, b, by rwa [mul_right_comm, mul_assoc]⟩
 #align is_coprime.of_mul_left_left IsCoprime.of_mul_left_left
 
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 theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z := by
   rw [mul_comm] at H; exact H.of_mul_left_left
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
 
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 theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y := by
   rw [isCoprime_comm] at H⊢; exact H.of_mul_left_left
 #align is_coprime.of_mul_right_left IsCoprime.of_mul_right_left
 
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 theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z := by
   rw [mul_comm] at H; exact H.of_mul_right_left
 #align is_coprime.of_mul_right_right IsCoprime.of_mul_right_right
 
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 theorem IsCoprime.mul_left_iff : IsCoprime (x * y) z ↔ IsCoprime x z ∧ IsCoprime y z :=
   ⟨fun H => ⟨H.of_mul_left_left, H.of_mul_left_right⟩, fun ⟨H1, H2⟩ => H1.mul_left H2⟩
 #align is_coprime.mul_left_iff IsCoprime.mul_left_iff
 
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 theorem IsCoprime.mul_right_iff : IsCoprime x (y * z) ↔ IsCoprime x y ∧ IsCoprime x z := by
   rw [isCoprime_comm, IsCoprime.mul_left_iff, isCoprime_comm, @isCoprime_comm _ _ z]
 #align is_coprime.mul_right_iff IsCoprime.mul_right_iff
@@ -284,12 +194,6 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
 #align is_coprime.is_unit_of_dvd' IsCoprime.isUnit_of_dvd'
 -/
 
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 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=
   let ⟨a, b, h⟩ := H
@@ -298,12 +202,6 @@ theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R 
 
 variable {x y z}
 
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 theorem IsCoprime.of_add_mul_left_left (h : IsCoprime (x + y * z) y) : IsCoprime x y :=
   let ⟨a, b, H⟩ := h
   ⟨a, a * z + b, by
@@ -311,72 +209,30 @@ theorem IsCoprime.of_add_mul_left_left (h : IsCoprime (x + y * z) y) : IsCoprime
       mul_left_comm] using H⟩
 #align is_coprime.of_add_mul_left_left IsCoprime.of_add_mul_left_left
 
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 theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y := by
   rw [mul_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
 
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 theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y := by
   rw [isCoprime_comm] at h⊢; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_right
 
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-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z x))) -> (IsCoprime.{u1} R _inst_1 x y)
-Case conversion may be inaccurate. Consider using '#align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_rightₓ'. -/
 theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y := by
   rw [mul_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_right
 
-/- warning: is_coprime.of_mul_add_left_left -> IsCoprime.of_mul_add_left_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_leftₓ'. -/
 theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y := by
   rw [add_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_left
 
-/- warning: is_coprime.of_mul_add_right_left -> IsCoprime.of_mul_add_right_left is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z y) x) y) -> (IsCoprime.{u1} R _inst_1 x y)
-Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_leftₓ'. -/
 theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y := by
   rw [add_comm] at h; exact h.of_add_mul_right_left
 #align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_left
 
-/- warning: is_coprime.of_mul_add_left_right -> IsCoprime.of_mul_add_left_right is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x z) y)) -> (IsCoprime.{u1} R _inst_1 x y)
-Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_rightₓ'. -/
 theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y := by
   rw [add_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_right
 
-/- warning: is_coprime.of_mul_add_right_right -> IsCoprime.of_mul_add_right_right is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z x) y)) -> (IsCoprime.{u1} R _inst_1 x y)
-Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_rightₓ'. -/
 theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y := by
   rw [add_comm] at h; exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
@@ -388,33 +244,15 @@ section ScalarTower
 variable {R G : Type _} [CommSemiring R] [Group G] [MulAction G R] [SMulCommClass G R R]
   [IsScalarTower G R R] (x : G) (y z : R)
 
-/- warning: is_coprime_group_smul_left -> isCoprime_group_smul_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {G : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Group.{u2} G] [_inst_3 : MulAction.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))] [_inst_4 : SMulCommClass.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))] [_inst_5 : IsScalarTower.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u1} R _inst_1 (SMul.smul.{u2, u1} G R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) x y) z) (IsCoprime.{u1} R _inst_1 y z)
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-  forall {R : Type.{u2}} {G : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Group.{u1} G] [_inst_3 : MulAction.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))] [_inst_4 : SMulCommClass.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))] [_inst_5 : IsScalarTower.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} G R R (instHSMul.{u1, u2} G R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)) x y) z) (IsCoprime.{u2} R _inst_1 y z)
-Case conversion may be inaccurate. Consider using '#align is_coprime_group_smul_left isCoprime_group_smul_leftₓ'. -/
 theorem isCoprime_group_smul_left : IsCoprime (x • y) z ↔ IsCoprime y z :=
   ⟨fun ⟨a, b, h⟩ => ⟨x • a, b, by rwa [smul_mul_assoc, ← mul_smul_comm]⟩, fun ⟨a, b, h⟩ =>
     ⟨x⁻¹ • a, b, by rwa [smul_mul_smul, inv_mul_self, one_smul]⟩⟩
 #align is_coprime_group_smul_left isCoprime_group_smul_left
 
-/- warning: is_coprime_group_smul_right -> isCoprime_group_smul_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {G : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Group.{u2} G] [_inst_3 : MulAction.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))] [_inst_4 : SMulCommClass.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))] [_inst_5 : IsScalarTower.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u1} R _inst_1 y (SMul.smul.{u2, u1} G R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) x z)) (IsCoprime.{u1} R _inst_1 y z)
-but is expected to have type
-  forall {R : Type.{u2}} {G : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Group.{u1} G] [_inst_3 : MulAction.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))] [_inst_4 : SMulCommClass.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))] [_inst_5 : IsScalarTower.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u2} R _inst_1 y (HSMul.hSMul.{u1, u2, u2} G R R (instHSMul.{u1, u2} G R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)) x z)) (IsCoprime.{u2} R _inst_1 y z)
-Case conversion may be inaccurate. Consider using '#align is_coprime_group_smul_right isCoprime_group_smul_rightₓ'. -/
 theorem isCoprime_group_smul_right : IsCoprime y (x • z) ↔ IsCoprime y z :=
   isCoprime_comm.trans <| (isCoprime_group_smul_left x z y).trans isCoprime_comm
 #align is_coprime_group_smul_right isCoprime_group_smul_right
 
-/- warning: is_coprime_group_smul -> isCoprime_group_smul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {G : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Group.{u2} G] [_inst_3 : MulAction.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))] [_inst_4 : SMulCommClass.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))] [_inst_5 : IsScalarTower.{u2, u1, u1} G R R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u1} R _inst_1 (SMul.smul.{u2, u1} G R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) x y) (SMul.smul.{u2, u1} G R (MulAction.toHasSmul.{u2, u1} G R (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) _inst_3) x z)) (IsCoprime.{u1} R _inst_1 y z)
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-  forall {R : Type.{u2}} {G : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Group.{u1} G] [_inst_3 : MulAction.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))] [_inst_4 : SMulCommClass.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))] [_inst_5 : IsScalarTower.{u1, u2, u2} G R R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3) (MulAction.toSMul.{u2, u2} R R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Monoid.toMulAction.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)] (x : G) (y : R) (z : R), Iff (IsCoprime.{u2} R _inst_1 (HSMul.hSMul.{u1, u2, u2} G R R (instHSMul.{u1, u2} G R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)) x y) (HSMul.hSMul.{u1, u2, u2} G R R (instHSMul.{u1, u2} G R (MulAction.toSMul.{u1, u2} G R (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)) _inst_3)) x z)) (IsCoprime.{u2} R _inst_1 y z)
-Case conversion may be inaccurate. Consider using '#align is_coprime_group_smul isCoprime_group_smulₓ'. -/
 theorem isCoprime_group_smul : IsCoprime (x • y) (x • z) ↔ IsCoprime y z :=
   (isCoprime_group_smul_left x y (x • z)).trans (isCoprime_group_smul_right x y z)
 #align is_coprime_group_smul isCoprime_group_smul
@@ -425,64 +263,28 @@ section CommSemiringUnit
 
 variable {R : Type _} [CommSemiring R] {x : R} (hu : IsUnit x) (y z : R)
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_left_left isCoprime_mul_unit_left_leftₓ'. -/
 theorem isCoprime_mul_unit_left_left : IsCoprime (x * y) z ↔ IsCoprime y z :=
   let ⟨u, hu⟩ := hu
   hu ▸ isCoprime_group_smul_left u y z
 #align is_coprime_mul_unit_left_left isCoprime_mul_unit_left_left
 
-/- warning: is_coprime_mul_unit_left_right -> isCoprime_mul_unit_left_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_left_right isCoprime_mul_unit_left_rightₓ'. -/
 theorem isCoprime_mul_unit_left_right : IsCoprime y (x * z) ↔ IsCoprime y z :=
   let ⟨u, hu⟩ := hu
   hu ▸ isCoprime_group_smul_right u y z
 #align is_coprime_mul_unit_left_right isCoprime_mul_unit_left_right
 
-/- warning: is_coprime_mul_unit_left -> isCoprime_mul_unit_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_left isCoprime_mul_unit_leftₓ'. -/
 theorem isCoprime_mul_unit_left : IsCoprime (x * y) (x * z) ↔ IsCoprime y z :=
   (isCoprime_mul_unit_left_left hu y (x * z)).trans (isCoprime_mul_unit_left_right hu y z)
 #align is_coprime_mul_unit_left isCoprime_mul_unit_left
 
-/- warning: is_coprime_mul_unit_right_left -> isCoprime_mul_unit_right_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_right_left isCoprime_mul_unit_right_leftₓ'. -/
 theorem isCoprime_mul_unit_right_left : IsCoprime (y * x) z ↔ IsCoprime y z :=
   mul_comm x y ▸ isCoprime_mul_unit_left_left hu y z
 #align is_coprime_mul_unit_right_left isCoprime_mul_unit_right_left
 
-/- warning: is_coprime_mul_unit_right_right -> isCoprime_mul_unit_right_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_right_right isCoprime_mul_unit_right_rightₓ'. -/
 theorem isCoprime_mul_unit_right_right : IsCoprime y (z * x) ↔ IsCoprime y z :=
   mul_comm x z ▸ isCoprime_mul_unit_left_right hu y z
 #align is_coprime_mul_unit_right_right isCoprime_mul_unit_right_right
 
-/- warning: is_coprime_mul_unit_right -> isCoprime_mul_unit_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime_mul_unit_right isCoprime_mul_unit_rightₓ'. -/
 theorem isCoprime_mul_unit_right : IsCoprime (y * x) (z * x) ↔ IsCoprime y z :=
   (isCoprime_mul_unit_right_left hu y (z * x)).trans (isCoprime_mul_unit_right_right hu y z)
 #align is_coprime_mul_unit_right isCoprime_mul_unit_right
@@ -495,172 +297,70 @@ section CommRing
 
 variable {R : Type u} [CommRing R]
 
-/- warning: is_coprime.add_mul_left_left -> IsCoprime.add_mul_left_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_left_left IsCoprime.add_mul_left_leftₓ'. -/
 theorem add_mul_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + y * z) y :=
   @of_add_mul_left_left R _ _ _ (-z) <| by simpa only [mul_neg, add_neg_cancel_right] using h
 #align is_coprime.add_mul_left_left IsCoprime.add_mul_left_left
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_right_left IsCoprime.add_mul_right_leftₓ'. -/
 theorem add_mul_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + z * y) y := by
   rw [mul_comm]; exact h.add_mul_left_left z
 #align is_coprime.add_mul_right_left IsCoprime.add_mul_right_left
 
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 theorem add_mul_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + x * z) := by
   rw [isCoprime_comm]; exact h.symm.add_mul_left_left z
 #align is_coprime.add_mul_left_right IsCoprime.add_mul_left_right
 
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 theorem add_mul_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + z * x) := by
   rw [isCoprime_comm]; exact h.symm.add_mul_right_left z
 #align is_coprime.add_mul_right_right IsCoprime.add_mul_right_right
 
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 theorem mul_add_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (y * z + x) y := by
   rw [add_comm]; exact h.add_mul_left_left z
 #align is_coprime.mul_add_left_left IsCoprime.mul_add_left_left
 
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 theorem mul_add_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (z * y + x) y := by
   rw [add_comm]; exact h.add_mul_right_left z
 #align is_coprime.mul_add_right_left IsCoprime.mul_add_right_left
 
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 theorem mul_add_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (x * z + y) := by
   rw [add_comm]; exact h.add_mul_left_right z
 #align is_coprime.mul_add_left_right IsCoprime.mul_add_left_right
 
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 theorem mul_add_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (z * x + y) := by
   rw [add_comm]; exact h.add_mul_right_right z
 #align is_coprime.mul_add_right_right IsCoprime.mul_add_right_right
 
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 theorem add_mul_left_left_iff {x y z : R} : IsCoprime (x + y * z) y ↔ IsCoprime x y :=
   ⟨of_add_mul_left_left, fun h => h.add_mul_left_left z⟩
 #align is_coprime.add_mul_left_left_iff IsCoprime.add_mul_left_left_iff
 
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 theorem add_mul_right_left_iff {x y z : R} : IsCoprime (x + z * y) y ↔ IsCoprime x y :=
   ⟨of_add_mul_right_left, fun h => h.add_mul_right_left z⟩
 #align is_coprime.add_mul_right_left_iff IsCoprime.add_mul_right_left_iff
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_left_right_iff IsCoprime.add_mul_left_right_iffₓ'. -/
 theorem add_mul_left_right_iff {x y z : R} : IsCoprime x (y + x * z) ↔ IsCoprime x y :=
   ⟨of_add_mul_left_right, fun h => h.add_mul_left_right z⟩
 #align is_coprime.add_mul_left_right_iff IsCoprime.add_mul_left_right_iff
 
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-Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_right_right_iff IsCoprime.add_mul_right_right_iffₓ'. -/
 theorem add_mul_right_right_iff {x y z : R} : IsCoprime x (y + z * x) ↔ IsCoprime x y :=
   ⟨of_add_mul_right_right, fun h => h.add_mul_right_right z⟩
 #align is_coprime.add_mul_right_right_iff IsCoprime.add_mul_right_right_iff
 
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 theorem mul_add_left_left_iff {x y z : R} : IsCoprime (y * z + x) y ↔ IsCoprime x y :=
   ⟨of_mul_add_left_left, fun h => h.mul_add_left_left z⟩
 #align is_coprime.mul_add_left_left_iff IsCoprime.mul_add_left_left_iff
 
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 theorem mul_add_right_left_iff {x y z : R} : IsCoprime (z * y + x) y ↔ IsCoprime x y :=
   ⟨of_mul_add_right_left, fun h => h.mul_add_right_left z⟩
 #align is_coprime.mul_add_right_left_iff IsCoprime.mul_add_right_left_iff
 
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 theorem mul_add_left_right_iff {x y z : R} : IsCoprime x (x * z + y) ↔ IsCoprime x y :=
   ⟨of_mul_add_left_right, fun h => h.mul_add_left_right z⟩
 #align is_coprime.mul_add_left_right_iff IsCoprime.mul_add_left_right_iff
 
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 theorem mul_add_right_right_iff {x y z : R} : IsCoprime x (z * x + y) ↔ IsCoprime x y :=
   ⟨of_mul_add_right_right, fun h => h.mul_add_right_right z⟩
 #align is_coprime.mul_add_right_right_iff IsCoprime.mul_add_right_right_iff
 
-/- warning: is_coprime.neg_left -> IsCoprime.neg_left is a dubious translation:
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 theorem neg_left {x y : R} (h : IsCoprime x y) : IsCoprime (-x) y :=
   by
   obtain ⟨a, b, h⟩ := h
@@ -668,64 +368,28 @@ theorem neg_left {x y : R} (h : IsCoprime x y) : IsCoprime (-x) y :=
   rwa [neg_mul_neg]
 #align is_coprime.neg_left IsCoprime.neg_left
 
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 theorem neg_left_iff (x y : R) : IsCoprime (-x) y ↔ IsCoprime x y :=
   ⟨fun h => neg_neg x ▸ h.neg_left, neg_left⟩
 #align is_coprime.neg_left_iff IsCoprime.neg_left_iff
 
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 theorem neg_right {x y : R} (h : IsCoprime x y) : IsCoprime x (-y) :=
   h.symm.neg_left.symm
 #align is_coprime.neg_right IsCoprime.neg_right
 
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 theorem neg_right_iff (x y : R) : IsCoprime x (-y) ↔ IsCoprime x y :=
   ⟨fun h => neg_neg y ▸ h.neg_right, neg_right⟩
 #align is_coprime.neg_right_iff IsCoprime.neg_right_iff
 
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 theorem neg_neg {x y : R} (h : IsCoprime x y) : IsCoprime (-x) (-y) :=
   h.neg_left.neg_right
 #align is_coprime.neg_neg IsCoprime.neg_neg
 
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 theorem neg_neg_iff (x y : R) : IsCoprime (-x) (-y) ↔ IsCoprime x y :=
   (neg_left_iff _ _).trans (neg_right_iff _ _)
 #align is_coprime.neg_neg_iff IsCoprime.neg_neg_iff
 
 end CommRing
 
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-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : R} {b : R}, (IsCoprime.{u1} R (StrictOrderedCommSemiring.toCommSemiring.{u1} R (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} R _inst_1))) a b) -> (Ne.{succ u1} R (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) a (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1)))))) b (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : LinearOrderedCommRing.{u1} R] {a : R} {b : R}, (IsCoprime.{u1} R (StrictOrderedCommSemiring.toCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))) a b) -> (Ne.{succ u1} R (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (StrictOrderedRing.toRing.{u1} R (LinearOrderedRing.toStrictOrderedRing.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1)))))))) a (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (StrictOrderedSemiring.toSemiring.{u1} R (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} R (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1)))))))) b (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (StrictOrderedCommSemiring.toCommSemiring.{u1} R (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} R (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u1} R _inst_1))) (LinearOrderedRing.isDomain.{u1} R (LinearOrderedCommRing.toLinearOrderedRing.{u1} R _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align is_coprime.sq_add_sq_ne_zero IsCoprime.sq_add_sq_ne_zeroₓ'. -/
 theorem sq_add_sq_ne_zero {R : Type _} [LinearOrderedCommRing R] {a b : R} (h : IsCoprime a b) :
     a ^ 2 + b ^ 2 ≠ 0 := by
   intro h'

448144f7

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -108,10 +108,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Nontrivial.{u1} R] {p : (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> R}, (IsCoprime.{u1} R _inst_1 (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFinHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) 0))) (p (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFinHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) 1)))) -> (Ne.{succ u1} ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> R) p (OfNat.ofNat.{u1} ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> R) 0 (Zero.toOfNat0.{u1} ((Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) -> R) (Pi.instZero.{0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a._@.Mathlib.RingTheory.Coprime.Basic._hyg.535 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => R) (fun (i : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_coprime.ne_zero IsCoprime.ne_zeroₓ'. -/
 /-- If a 2-vector `p` satisfies `is_coprime (p 0) (p 1)`, then `p ≠ 0`. -/
-theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 :=
-  by
-  rintro rfl
-  exact not_isCoprime_zero_zero h
+theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 := by
+  rintro rfl; exact not_isCoprime_zero_zero h
 #align is_coprime.ne_zero IsCoprime.ne_zero
 
 #print isCoprime_one_left /-
@@ -176,10 +174,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x y) -> (IsCoprime.{u1} R _inst_1 x z) -> (IsCoprime.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y z))
 Case conversion may be inaccurate. Consider using '#align is_coprime.mul_right IsCoprime.mul_rightₓ'. -/
-theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) :=
-  by
-  rw [isCoprime_comm] at H1 H2⊢
-  exact H1.mul_left H2
+theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by
+  rw [isCoprime_comm] at H1 H2⊢; exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
 /- warning: is_coprime.mul_dvd -> IsCoprime.mul_dvd is a dubious translation:
@@ -216,10 +212,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x y) z) -> (IsCoprime.{u1} R _inst_1 y z)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_left_right IsCoprime.of_mul_left_rightₓ'. -/
-theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z :=
-  by
-  rw [mul_comm] at H
-  exact H.of_mul_left_left
+theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z := by
+  rw [mul_comm] at H; exact H.of_mul_left_left
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
 
 /- warning: is_coprime.of_mul_right_left -> IsCoprime.of_mul_right_left is a dubious translation:
@@ -228,10 +222,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y z)) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_right_left IsCoprime.of_mul_right_leftₓ'. -/
-theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y :=
-  by
-  rw [isCoprime_comm] at H⊢
-  exact H.of_mul_left_left
+theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y := by
+  rw [isCoprime_comm] at H⊢; exact H.of_mul_left_left
 #align is_coprime.of_mul_right_left IsCoprime.of_mul_right_left
 
 /- warning: is_coprime.of_mul_right_right -> IsCoprime.of_mul_right_right is a dubious translation:
@@ -240,10 +232,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y z)) -> (IsCoprime.{u1} R _inst_1 x z)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_right_right IsCoprime.of_mul_right_rightₓ'. -/
-theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z :=
-  by
-  rw [mul_comm] at H
-  exact H.of_mul_right_left
+theorem IsCoprime.of_mul_right_right (H : IsCoprime x (y * z)) : IsCoprime x z := by
+  rw [mul_comm] at H; exact H.of_mul_right_left
 #align is_coprime.of_mul_right_right IsCoprime.of_mul_right_right
 
 /- warning: is_coprime.mul_left_iff -> IsCoprime.mul_left_iff is a dubious translation:
@@ -327,10 +317,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z y)) y) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_leftₓ'. -/
-theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y :=
-  by
-  rw [mul_comm] at h
-  exact h.of_add_mul_left_left
+theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprime x y := by
+  rw [mul_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
 
 /- warning: is_coprime.of_add_mul_left_right -> IsCoprime.of_add_mul_left_right is a dubious translation:
@@ -339,10 +327,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x z))) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_rightₓ'. -/
-theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y :=
-  by
-  rw [isCoprime_comm] at h⊢
-  exact h.of_add_mul_left_left
+theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y := by
+  rw [isCoprime_comm] at h⊢; exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_right
 
 /- warning: is_coprime.of_add_mul_right_right -> IsCoprime.of_add_mul_right_right is a dubious translation:
@@ -351,10 +337,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z x))) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_rightₓ'. -/
-theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y :=
-  by
-  rw [mul_comm] at h
-  exact h.of_add_mul_left_right
+theorem IsCoprime.of_add_mul_right_right (h : IsCoprime x (y + z * x)) : IsCoprime x y := by
+  rw [mul_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_add_mul_right_right IsCoprime.of_add_mul_right_right
 
 /- warning: is_coprime.of_mul_add_left_left -> IsCoprime.of_mul_add_left_left is a dubious translation:
@@ -363,10 +347,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) y z) x) y) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_leftₓ'. -/
-theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y :=
-  by
-  rw [add_comm] at h
-  exact h.of_add_mul_left_left
+theorem IsCoprime.of_mul_add_left_left (h : IsCoprime (y * z + x) y) : IsCoprime x y := by
+  rw [add_comm] at h; exact h.of_add_mul_left_left
 #align is_coprime.of_mul_add_left_left IsCoprime.of_mul_add_left_left
 
 /- warning: is_coprime.of_mul_add_right_left -> IsCoprime.of_mul_add_right_left is a dubious translation:
@@ -375,10 +357,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z y) x) y) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_leftₓ'. -/
-theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y :=
-  by
-  rw [add_comm] at h
-  exact h.of_add_mul_right_left
+theorem IsCoprime.of_mul_add_right_left (h : IsCoprime (z * y + x) y) : IsCoprime x y := by
+  rw [add_comm] at h; exact h.of_add_mul_right_left
 #align is_coprime.of_mul_add_right_left IsCoprime.of_mul_add_right_left
 
 /- warning: is_coprime.of_mul_add_left_right -> IsCoprime.of_mul_add_left_right is a dubious translation:
@@ -387,10 +367,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) x z) y)) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_rightₓ'. -/
-theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y :=
-  by
-  rw [add_comm] at h
-  exact h.of_add_mul_left_right
+theorem IsCoprime.of_mul_add_left_right (h : IsCoprime x (x * z + y)) : IsCoprime x y := by
+  rw [add_comm] at h; exact h.of_add_mul_left_right
 #align is_coprime.of_mul_add_left_right IsCoprime.of_mul_add_left_right
 
 /- warning: is_coprime.of_mul_add_right_right -> IsCoprime.of_mul_add_right_right is a dubious translation:
@@ -399,10 +377,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R} {z : R}, (IsCoprime.{u1} R _inst_1 x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) z x) y)) -> (IsCoprime.{u1} R _inst_1 x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_rightₓ'. -/
-theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y :=
-  by
-  rw [add_comm] at h
-  exact h.of_add_mul_right_right
+theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCoprime x y := by
+  rw [add_comm] at h; exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
 
 end CommSemiring
@@ -535,10 +511,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) x (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) z y)) y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_right_left IsCoprime.add_mul_right_leftₓ'. -/
-theorem add_mul_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + z * y) y :=
-  by
-  rw [mul_comm]
-  exact h.add_mul_left_left z
+theorem add_mul_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (x + z * y) y := by
+  rw [mul_comm]; exact h.add_mul_left_left z
 #align is_coprime.add_mul_right_left IsCoprime.add_mul_right_left
 
 /- warning: is_coprime.add_mul_left_right -> IsCoprime.add_mul_left_right is a dubious translation:
@@ -547,10 +521,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x z)))
 Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_left_right IsCoprime.add_mul_left_rightₓ'. -/
-theorem add_mul_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + x * z) :=
-  by
-  rw [isCoprime_comm]
-  exact h.symm.add_mul_left_left z
+theorem add_mul_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + x * z) := by
+  rw [isCoprime_comm]; exact h.symm.add_mul_left_left z
 #align is_coprime.add_mul_left_right IsCoprime.add_mul_left_right
 
 /- warning: is_coprime.add_mul_right_right -> IsCoprime.add_mul_right_right is a dubious translation:
@@ -559,10 +531,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) y (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) z x)))
 Case conversion may be inaccurate. Consider using '#align is_coprime.add_mul_right_right IsCoprime.add_mul_right_rightₓ'. -/
-theorem add_mul_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + z * x) :=
-  by
-  rw [isCoprime_comm]
-  exact h.symm.add_mul_right_left z
+theorem add_mul_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (y + z * x) := by
+  rw [isCoprime_comm]; exact h.symm.add_mul_right_left z
 #align is_coprime.add_mul_right_right IsCoprime.add_mul_right_right
 
 /- warning: is_coprime.mul_add_left_left -> IsCoprime.mul_add_left_left is a dubious translation:
@@ -571,10 +541,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) y z) x) y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.mul_add_left_left IsCoprime.mul_add_left_leftₓ'. -/
-theorem mul_add_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (y * z + x) y :=
-  by
-  rw [add_comm]
-  exact h.add_mul_left_left z
+theorem mul_add_left_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (y * z + x) y := by
+  rw [add_comm]; exact h.add_mul_left_left z
 #align is_coprime.mul_add_left_left IsCoprime.mul_add_left_left
 
 /- warning: is_coprime.mul_add_right_left -> IsCoprime.mul_add_right_left is a dubious translation:
@@ -583,10 +551,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) z y) x) y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.mul_add_right_left IsCoprime.mul_add_right_leftₓ'. -/
-theorem mul_add_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (z * y + x) y :=
-  by
-  rw [add_comm]
-  exact h.add_mul_right_left z
+theorem mul_add_right_left {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime (z * y + x) y := by
+  rw [add_comm]; exact h.add_mul_right_left z
 #align is_coprime.mul_add_right_left IsCoprime.mul_add_right_left
 
 /- warning: is_coprime.mul_add_left_right -> IsCoprime.mul_add_left_right is a dubious translation:
@@ -595,10 +561,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x z) y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.mul_add_left_right IsCoprime.mul_add_left_rightₓ'. -/
-theorem mul_add_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (x * z + y) :=
-  by
-  rw [add_comm]
-  exact h.add_mul_left_right z
+theorem mul_add_left_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (x * z + y) := by
+  rw [add_comm]; exact h.add_mul_left_right z
 #align is_coprime.mul_add_left_right IsCoprime.mul_add_left_right
 
 /- warning: is_coprime.mul_add_right_right -> IsCoprime.mul_add_right_right is a dubious translation:
@@ -607,10 +571,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (forall (z : R), IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) z x) y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.mul_add_right_right IsCoprime.mul_add_right_rightₓ'. -/
-theorem mul_add_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (z * x + y) :=
-  by
-  rw [add_comm]
-  exact h.add_mul_right_right z
+theorem mul_add_right_right {x y : R} (h : IsCoprime x y) (z : R) : IsCoprime x (z * x + y) := by
+  rw [add_comm]; exact h.add_mul_right_right z
 #align is_coprime.mul_add_right_right IsCoprime.mul_add_right_right
 
 /- warning: is_coprime.add_mul_left_left_iff -> IsCoprime.add_mul_left_left_iff is a dubious translation:

448144f7

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -298,7 +298,7 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} S _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.map IsCoprime.mapₓ'. -/
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=

448144f7

bump to nightly-2023-03-27-02

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

0e4ebd8c

Diff

@@ -695,7 +695,7 @@ theorem mul_add_right_right_iff {x y z : R} : IsCoprime x (z * x + y) ↔ IsCopr
 
 /- warning: is_coprime.neg_left -> IsCoprime.neg_left is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) y)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) y)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x) y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_left IsCoprime.neg_leftₓ'. -/
@@ -708,7 +708,7 @@ theorem neg_left {x y : R} (h : IsCoprime x y) : IsCoprime (-x) y :=
 
 /- warning: is_coprime.neg_left_iff -> IsCoprime.neg_left_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) y) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) y) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x) y) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_left_iff IsCoprime.neg_left_iffₓ'. -/
@@ -718,7 +718,7 @@ theorem neg_left_iff (x y : R) : IsCoprime (-x) y ↔ IsCoprime x y :=
 
 /- warning: is_coprime.neg_right -> IsCoprime.neg_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_right IsCoprime.neg_rightₓ'. -/
@@ -728,7 +728,7 @@ theorem neg_right {x y : R} (h : IsCoprime x y) : IsCoprime x (-y) :=
 
 /- warning: is_coprime.neg_right_iff -> IsCoprime.neg_right_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_right_iff IsCoprime.neg_right_iffₓ'. -/
@@ -738,7 +738,7 @@ theorem neg_right_iff (x y : R) : IsCoprime x (-y) ↔ IsCoprime x y :=
 
 /- warning: is_coprime.neg_neg -> IsCoprime.neg_neg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y) -> (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_neg IsCoprime.neg_negₓ'. -/
@@ -748,7 +748,7 @@ theorem neg_neg {x y : R} (h : IsCoprime x y) : IsCoprime (-x) (-y) :=
 
 /- warning: is_coprime.neg_neg_iff -> IsCoprime.neg_neg_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (x : R) (y : R), Iff (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) x) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) y)) (IsCoprime.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) x y)
 Case conversion may be inaccurate. Consider using '#align is_coprime.neg_neg_iff IsCoprime.neg_neg_iffₓ'. -/

448144f7

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -298,7 +298,7 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} S _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.map IsCoprime.mapₓ'. -/
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=

448144f7

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -64,7 +64,7 @@ theorem isCoprime_comm : IsCoprime x y ↔ IsCoprime y x :=
 theorem isCoprime_self : IsCoprime x x ↔ IsUnit x :=
   ⟨fun ⟨a, b, h⟩ => isUnit_of_mul_eq_one x (a + b) <| by rwa [mul_comm, add_mul], fun h =>
     let ⟨b, hb⟩ := isUnit_iff_exists_inv'.1 h
-    ⟨b, 0, by rwa [zero_mul, add_zero]⟩⟩
+    ⟨b, 0, by rwa [MulZeroClass.zero_mul, add_zero]⟩⟩
 #align is_coprime_self isCoprime_self
 -/
 
@@ -75,7 +75,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R}, Iff (IsCoprime.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)))) x) (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) x)
 Case conversion may be inaccurate. Consider using '#align is_coprime_zero_left isCoprime_zero_leftₓ'. -/
 theorem isCoprime_zero_left : IsCoprime 0 x ↔ IsUnit x :=
-  ⟨fun ⟨a, b, H⟩ => isUnit_of_mul_eq_one x b <| by rwa [mul_zero, zero_add, mul_comm] at H, fun H =>
+  ⟨fun ⟨a, b, H⟩ =>
+    isUnit_of_mul_eq_one x b <| by rwa [MulZeroClass.mul_zero, zero_add, mul_comm] at H, fun H =>
     let ⟨b, hb⟩ := isUnit_iff_exists_inv'.1 H
     ⟨1, b, by rwa [one_mul, zero_add]⟩⟩
 #align is_coprime_zero_left isCoprime_zero_left
@@ -115,13 +116,13 @@ theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0)
 
 #print isCoprime_one_left /-
 theorem isCoprime_one_left : IsCoprime 1 x :=
-  ⟨1, 0, by rw [one_mul, zero_mul, add_zero]⟩
+  ⟨1, 0, by rw [one_mul, MulZeroClass.zero_mul, add_zero]⟩
 #align is_coprime_one_left isCoprime_one_left
 -/
 
 #print isCoprime_one_right /-
 theorem isCoprime_one_right : IsCoprime x 1 :=
-  ⟨0, 1, by rw [one_mul, zero_mul, zero_add]⟩
+  ⟨0, 1, by rw [one_mul, MulZeroClass.zero_mul, zero_add]⟩
 #align is_coprime_one_right isCoprime_one_right
 -/

448144f7

bump to nightly-2023-03-08-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

10f15343

Diff

@@ -297,7 +297,7 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} S _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) f y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {x : R} {y : R}, (IsCoprime.{u1} R _inst_1 x y) -> (forall {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))), IsCoprime.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) x) _inst_2 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) f y))
 Case conversion may be inaccurate. Consider using '#align is_coprime.map IsCoprime.mapₓ'. -/
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=

448144f7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

a95b16cb

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

@@ -13,20 +13,21 @@ import Mathlib.Tactic.Ring
 #align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"a95b16cbade0f938fc24abd05412bde1e84bab9b"
 
 /-!
-# Coprime elements of a ring
+# Coprime elements of a ring or monoid
 
-## Main definitions
+## Main definition
 
 * `IsCoprime x y`: that `x` and `y` are coprime, defined to be the existence of `a` and `b` such
-that `a * x + b * y = 1`. Note that elements with no common divisors are not necessarily coprime,
-e.g., the multivariate polynomials `x₁` and `x₂` are not coprime.
+that `a * x + b * y = 1`. Note that elements with no common divisors (`IsRelPrime`) are not
+necessarily coprime, e.g., the multivariate polynomials `x₁` and `x₂` are not coprime.
+The two notions are equivalent in Bézout rings, see `isRelPrime_iff_isCoprime`.
+
+This file also contains lemmas about `IsRelPrime` parallel to `IsCoprime`.
 
 See also `RingTheory.Coprime.Lemmas` for further development of coprime elements.
 -/
 
 
-open Classical
-
 universe u v
 
 section CommSemiring
@@ -98,14 +99,12 @@ theorem isCoprime_one_right : IsCoprime x 1 :=
   ⟨0, 1, by rw [one_mul, zero_mul, zero_add]⟩
 #align is_coprime_one_right isCoprime_one_right
 
-/-- See also `UniqueFactorizationMonoid.dvd_of_coprime_of_dvd_mul_right`. -/
 theorem IsCoprime.dvd_of_dvd_mul_right (H1 : IsCoprime x z) (H2 : x ∣ y * z) : x ∣ y := by
   let ⟨a, b, H⟩ := H1
   rw [← mul_one y, ← H, mul_add, ← mul_assoc, mul_left_comm]
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_right IsCoprime.dvd_of_dvd_mul_right
 
-/-- See also `UniqueFactorizationMonoid.dvd_of_coprime_of_dvd_mul_left`. -/
 theorem IsCoprime.dvd_of_dvd_mul_left (H1 : IsCoprime x y) (H2 : x ∣ y * z) : x ∣ z := by
   let ⟨a, b, H⟩ := H1
   rw [← one_mul z, ← H, add_mul, mul_right_comm, mul_assoc b]
@@ -129,7 +128,6 @@ theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprim
   exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
-/-- See also `UniqueFactorizationMonoid.mul_dvd`. -/
 theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x * y ∣ z := by
   obtain ⟨a, b, h⟩ := H
   rw [← mul_one z, ← h, mul_add]
@@ -187,6 +185,9 @@ theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a)
   (h.of_isCoprime_of_dvd_left ha).isUnit_of_dvd hb
 #align is_coprime.is_unit_of_dvd' IsCoprime.isUnit_of_dvd'
 
+theorem IsCoprime.isRelPrime {a b : R} (h : IsCoprime a b) : IsRelPrime a b :=
+  fun _ ↦ h.isUnit_of_dvd'
+
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=
   let ⟨a, b, h⟩ := H
@@ -235,6 +236,31 @@ theorem IsCoprime.of_mul_add_right_right (h : IsCoprime x (z * x + y)) : IsCopri
   exact h.of_add_mul_right_right
 #align is_coprime.of_mul_add_right_right IsCoprime.of_mul_add_right_right
 
+theorem IsRelPrime.of_add_mul_left_left (h : IsRelPrime (x + y * z) y) : IsRelPrime x y :=
+  fun _ hx hy ↦ h (dvd_add hx <| dvd_mul_of_dvd_left hy z) hy
+
+theorem IsRelPrime.of_add_mul_right_left (h : IsRelPrime (x + z * y) y) : IsRelPrime x y :=
+  (mul_comm z y ▸ h).of_add_mul_left_left
+
+theorem IsRelPrime.of_add_mul_left_right (h : IsRelPrime x (y + x * z)) : IsRelPrime x y := by
+  rw [isRelPrime_comm] at h ⊢
+  exact h.of_add_mul_left_left
+
+theorem IsRelPrime.of_add_mul_right_right (h : IsRelPrime x (y + z * x)) : IsRelPrime x y :=
+  (mul_comm z x ▸ h).of_add_mul_left_right
+
+theorem IsRelPrime.of_mul_add_left_left (h : IsRelPrime (y * z + x) y) : IsRelPrime x y :=
+  (add_comm _ x ▸ h).of_add_mul_left_left
+
+theorem IsRelPrime.of_mul_add_right_left (h : IsRelPrime (z * y + x) y) : IsRelPrime x y :=
+  (add_comm _ x ▸ h).of_add_mul_right_left
+
+theorem IsRelPrime.of_mul_add_left_right (h : IsRelPrime x (x * z + y)) : IsRelPrime x y :=
+  (add_comm _ y ▸ h).of_add_mul_left_right
+
+theorem IsRelPrime.of_mul_add_right_right (h : IsRelPrime x (z * x + y)) : IsRelPrime x y :=
+  (add_comm _ y ▸ h).of_add_mul_right_right
+
 end CommSemiring
 
 section ScalarTower
@@ -407,3 +433,72 @@ theorem sq_add_sq_ne_zero {R : Type*} [LinearOrderedCommRing R] {a b : R} (h : I
 #align is_coprime.sq_add_sq_ne_zero IsCoprime.sq_add_sq_ne_zero
 
 end IsCoprime
+
+namespace IsRelPrime
+
+variable {R} [CommRing R] {x y : R} (h : IsRelPrime x y) (z : R)
+
+theorem add_mul_left_left : IsRelPrime (x + y * z) y :=
+  @of_add_mul_left_left R _ _ _ (-z) <| by simpa only [mul_neg, add_neg_cancel_right] using h
+
+theorem add_mul_right_left : IsRelPrime (x + z * y) y :=
+  mul_comm z y ▸ h.add_mul_left_left z
+
+theorem add_mul_left_right : IsRelPrime x (y + x * z) :=
+  (h.symm.add_mul_left_left z).symm
+
+theorem add_mul_right_right : IsRelPrime x (y + z * x) :=
+  (h.symm.add_mul_right_left z).symm
+
+theorem mul_add_left_left : IsRelPrime (y * z + x) y :=
+  add_comm x _ ▸ h.add_mul_left_left z
+
+theorem mul_add_right_left : IsRelPrime (z * y + x) y :=
+  add_comm x _ ▸ h.add_mul_right_left z
+
+theorem mul_add_left_right : IsRelPrime x (x * z + y) :=
+  add_comm y _ ▸ h.add_mul_left_right z
+
+theorem mul_add_right_right : IsRelPrime x (z * x + y) :=
+  add_comm y _ ▸ h.add_mul_right_right z
+
+variable {z}
+
+theorem add_mul_left_left_iff : IsRelPrime (x + y * z) y ↔ IsRelPrime x y :=
+  ⟨of_add_mul_left_left, fun h ↦ h.add_mul_left_left z⟩
+
+theorem add_mul_right_left_iff : IsRelPrime (x + z * y) y ↔ IsRelPrime x y :=
+  ⟨of_add_mul_right_left, fun h ↦ h.add_mul_right_left z⟩
+
+theorem add_mul_left_right_iff : IsRelPrime x (y + x * z) ↔ IsRelPrime x y :=
+  ⟨of_add_mul_left_right, fun h ↦ h.add_mul_left_right z⟩
+
+theorem add_mul_right_right_iff : IsRelPrime x (y + z * x) ↔ IsRelPrime x y :=
+  ⟨of_add_mul_right_right, fun h ↦ h.add_mul_right_right z⟩
+
+theorem mul_add_left_left_iff {x y z : R} : IsRelPrime (y * z + x) y ↔ IsRelPrime x y :=
+  ⟨of_mul_add_left_left, fun h ↦ h.mul_add_left_left z⟩
+
+theorem mul_add_right_left_iff {x y z : R} : IsRelPrime (z * y + x) y ↔ IsRelPrime x y :=
+  ⟨of_mul_add_right_left, fun h ↦ h.mul_add_right_left z⟩
+
+theorem mul_add_left_right_iff {x y z : R} : IsRelPrime x (x * z + y) ↔ IsRelPrime x y :=
+  ⟨of_mul_add_left_right, fun h ↦ h.mul_add_left_right z⟩
+
+theorem mul_add_right_right_iff {x y z : R} : IsRelPrime x (z * x + y) ↔ IsRelPrime x y :=
+  ⟨of_mul_add_right_right, fun h ↦ h.mul_add_right_right z⟩
+
+theorem neg_left : IsRelPrime (-x) y := fun _ ↦ (h <| dvd_neg.mp ·)
+theorem neg_right : IsRelPrime x (-y) := h.symm.neg_left.symm
+protected theorem neg_neg : IsRelPrime (-x) (-y) := h.neg_left.neg_right
+
+theorem neg_left_iff (x y : R) : IsRelPrime (-x) y ↔ IsRelPrime x y :=
+  ⟨fun h ↦ neg_neg x ▸ h.neg_left, neg_left⟩
+
+theorem neg_right_iff (x y : R) : IsRelPrime x (-y) ↔ IsRelPrime x y :=
+  ⟨fun h ↦ neg_neg y ▸ h.neg_right, neg_right⟩
+
+theorem neg_neg_iff (x y : R) : IsRelPrime (-x) (-y) ↔ IsRelPrime x y :=
+  (neg_left_iff _ _).trans (neg_right_iff _ _)
+
+end IsRelPrime

a95b16cb

feat: a polynomial over a perfect field is separable iff it is square-free (#10170)

Yet another small step toward Jordan-Chevalley-Dunford.

This was far more work than expected, partly because of missing API for Squarefree, and partly because the definition IsCoprime is the wrong concept for unique factorization domains.

aec68874

Diff

@@ -98,12 +98,14 @@ theorem isCoprime_one_right : IsCoprime x 1 :=
   ⟨0, 1, by rw [one_mul, zero_mul, zero_add]⟩
 #align is_coprime_one_right isCoprime_one_right
 
+/-- See also `UniqueFactorizationMonoid.dvd_of_coprime_of_dvd_mul_right`. -/
 theorem IsCoprime.dvd_of_dvd_mul_right (H1 : IsCoprime x z) (H2 : x ∣ y * z) : x ∣ y := by
   let ⟨a, b, H⟩ := H1
   rw [← mul_one y, ← H, mul_add, ← mul_assoc, mul_left_comm]
   exact dvd_add (dvd_mul_left _ _) (H2.mul_left _)
 #align is_coprime.dvd_of_dvd_mul_right IsCoprime.dvd_of_dvd_mul_right
 
+/-- See also `UniqueFactorizationMonoid.dvd_of_coprime_of_dvd_mul_left`. -/
 theorem IsCoprime.dvd_of_dvd_mul_left (H1 : IsCoprime x y) (H2 : x ∣ y * z) : x ∣ z := by
   let ⟨a, b, H⟩ := H1
   rw [← one_mul z, ← H, add_mul, mul_right_comm, mul_assoc b]
@@ -127,6 +129,7 @@ theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprim
   exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
+/-- See also `UniqueFactorizationMonoid.mul_dvd`. -/
 theorem IsCoprime.mul_dvd (H : IsCoprime x y) (H1 : x ∣ z) (H2 : y ∣ z) : x * y ∣ z := by
   obtain ⟨a, b, h⟩ := H
   rw [← mul_one z, ← h, mul_add]

a95b16cb

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -7,6 +7,7 @@ import Mathlib.Algebra.GroupPower.Ring
 import Mathlib.Algebra.Ring.Divisibility.Basic
 import Mathlib.Algebra.Ring.Hom.Defs
 import Mathlib.GroupTheory.GroupAction.Units
+import Mathlib.Logic.Basic
 import Mathlib.Tactic.Ring
 
 #align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"a95b16cbade0f938fc24abd05412bde1e84bab9b"

a95b16cb

refactor(Algebra/Hom): transpose Hom and file name (#8095)

I believe the file defining a type of morphisms belongs alongside the file defining the structure this morphism works on. So I would like to reorganize the files in the Mathlib.Algebra.Hom folder so that e.g. Mathlib.Algebra.Hom.Ring becomes Mathlib.Algebra.Ring.Hom and Mathlib.Algebra.Hom.NonUnitalAlg becomes Mathlib.Algebra.Algebra.NonUnitalHom.

While fixing the imports I went ahead and sorted them for good luck.

The full list of changes is: renamed: Mathlib/Algebra/Hom/NonUnitalAlg.lean -> Mathlib/Algebra/Algebra/NonUnitalHom.lean renamed: Mathlib/Algebra/Hom/Aut.lean -> Mathlib/Algebra/Group/Aut.lean renamed: Mathlib/Algebra/Hom/Commute.lean -> Mathlib/Algebra/Group/Commute/Hom.lean renamed: Mathlib/Algebra/Hom/Embedding.lean -> Mathlib/Algebra/Group/Embedding.lean renamed: Mathlib/Algebra/Hom/Equiv/Basic.lean -> Mathlib/Algebra/Group/Equiv/Basic.lean renamed: Mathlib/Algebra/Hom/Equiv/TypeTags.lean -> Mathlib/Algebra/Group/Equiv/TypeTags.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/Basic.lean -> Mathlib/Algebra/Group/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean -> Mathlib/Algebra/GroupWithZero/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Freiman.lean -> Mathlib/Algebra/Group/Freiman.lean renamed: Mathlib/Algebra/Hom/Group/Basic.lean -> Mathlib/Algebra/Group/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Group/Defs.lean -> Mathlib/Algebra/Group/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/GroupAction.lean -> Mathlib/GroupTheory/GroupAction/Hom.lean renamed: Mathlib/Algebra/Hom/GroupInstances.lean -> Mathlib/Algebra/Group/Hom/Instances.lean renamed: Mathlib/Algebra/Hom/Iterate.lean -> Mathlib/Algebra/GroupPower/IterateHom.lean renamed: Mathlib/Algebra/Hom/Centroid.lean -> Mathlib/Algebra/Ring/CentroidHom.lean renamed: Mathlib/Algebra/Hom/Ring/Basic.lean -> Mathlib/Algebra/Ring/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Ring/Defs.lean -> Mathlib/Algebra/Ring/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/Units.lean -> Mathlib/Algebra/Group/Units/Hom.lean

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reorganizing.20.60Mathlib.2EAlgebra.2EHom.60

92fe122e

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Ken Lee, Chris Hughes
 -/
-import Mathlib.Tactic.Ring
-import Mathlib.GroupTheory.GroupAction.Units
-import Mathlib.Algebra.Ring.Divisibility.Basic
-import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.GroupPower.Ring
+import Mathlib.Algebra.Ring.Divisibility.Basic
+import Mathlib.Algebra.Ring.Hom.Defs
+import Mathlib.GroupTheory.GroupAction.Units
+import Mathlib.Tactic.Ring
 
 #align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"a95b16cbade0f938fc24abd05412bde1e84bab9b"

a95b16cb

feat: Chinese remainder for ZMod. (#7599)

201c8eea

Diff

@@ -71,6 +71,13 @@ theorem not_isCoprime_zero_zero [Nontrivial R] : ¬IsCoprime (0 : R) 0 :=
   mt isCoprime_zero_right.mp not_isUnit_zero
 #align not_coprime_zero_zero not_isCoprime_zero_zero
 
+lemma IsCoprime.intCast {R : Type*} [CommRing R] {a b : ℤ} (h : IsCoprime a b) :
+    IsCoprime (a : R) (b : R) := by
+  rcases h with ⟨u, v, H⟩
+  use u, v
+  rw_mod_cast [H]
+  exact Int.cast_one
+
 /-- If a 2-vector `p` satisfies `IsCoprime (p 0) (p 1)`, then `p ≠ 0`. -/
 theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 := by
   rintro rfl

a95b16cb

feat: lemmas about divisibility, mostly related to nilpotency (#7355)

bf1ceb82

Diff

@@ -5,7 +5,7 @@ Authors: Kenny Lau, Ken Lee, Chris Hughes
 -/
 import Mathlib.Tactic.Ring
 import Mathlib.GroupTheory.GroupAction.Units
-import Mathlib.Algebra.Ring.Divisibility
+import Mathlib.Algebra.Ring.Divisibility.Basic
 import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.GroupPower.Ring

a95b16cb

refactor: split Algebra.Hom.Group and Algebra.Hom.Ring (#7094)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

260cb506

Diff

@@ -6,7 +6,7 @@ Authors: Kenny Lau, Ken Lee, Chris Hughes
 import Mathlib.Tactic.Ring
 import Mathlib.GroupTheory.GroupAction.Units
 import Mathlib.Algebra.Ring.Divisibility
-import Mathlib.Algebra.Hom.Ring
+import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.GroupPower.Ring
 
 #align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"a95b16cbade0f938fc24abd05412bde1e84bab9b"

a95b16cb

feat: add some symm attributes throughout the library (#6708)

Also add a couple of refl and trans attributes

20d6b8e6

Diff

@@ -41,6 +41,7 @@ def IsCoprime : Prop :=
 
 variable {x y z}
 
+@[symm]
 theorem IsCoprime.symm (H : IsCoprime x y) : IsCoprime y x :=
   let ⟨a, b, H⟩ := H
   ⟨b, a, by rw [add_comm, H]⟩

a95b16cb

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

@@ -227,7 +227,7 @@ end CommSemiring
 
 section ScalarTower
 
-variable {R G : Type _} [CommSemiring R] [Group G] [MulAction G R] [SMulCommClass G R R]
+variable {R G : Type*} [CommSemiring R] [Group G] [MulAction G R] [SMulCommClass G R R]
   [IsScalarTower G R R] (x : G) (y z : R)
 
 theorem isCoprime_group_smul_left : IsCoprime (x • y) z ↔ IsCoprime y z :=
@@ -247,7 +247,7 @@ end ScalarTower
 
 section CommSemiringUnit
 
-variable {R : Type _} [CommSemiring R] {x : R} (hu : IsUnit x) (y z : R)
+variable {R : Type*} [CommSemiring R] {x : R} (hu : IsUnit x) (y z : R)
 
 theorem isCoprime_mul_unit_left_left : IsCoprime (x * y) z ↔ IsCoprime y z :=
   let ⟨u, hu⟩ := hu
@@ -382,7 +382,7 @@ theorem neg_neg_iff (x y : R) : IsCoprime (-x) (-y) ↔ IsCoprime x y :=
 
 end CommRing
 
-theorem sq_add_sq_ne_zero {R : Type _} [LinearOrderedCommRing R] {a b : R} (h : IsCoprime a b) :
+theorem sq_add_sq_ne_zero {R : Type*} [LinearOrderedCommRing R] {a b : R} (h : IsCoprime a b) :
     a ^ 2 + b ^ 2 ≠ 0 := by
   intro h'
   obtain ⟨ha, hb⟩ := (add_eq_zero_iff'

a95b16cb

feat(AlgebraicGeometry/EllipticCurve/Weierstrass): elliptic curves with specified j-invariant (#5935)

Main changes:

Define specific Weierstrass curves, whose j-invariants should be 0, 1728, or ≠ 0 and 1728.
Prove the quantities c₄, Δ and j for them (whenever they are defined).
Define an elliptic curve from an element j in a field, whose j-invariant is equal to j.
Generalize Inhabited (EllipticCurve ℚ) to Inhabited (EllipticCurve F) for any field F (computable if F has DecidableEq).

06ace73a

Diff

@@ -76,6 +76,11 @@ theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0)
   exact not_isCoprime_zero_zero h
 #align is_coprime.ne_zero IsCoprime.ne_zero
 
+theorem IsCoprime.ne_zero_or_ne_zero [Nontrivial R] (h : IsCoprime x y) : x ≠ 0 ∨ y ≠ 0 := by
+  apply not_or_of_imp
+  rintro rfl rfl
+  exact not_isCoprime_zero_zero h
+
 theorem isCoprime_one_left : IsCoprime 1 x :=
   ⟨1, 0, by rw [one_mul, zero_mul, add_zero]⟩
 #align is_coprime_one_left isCoprime_one_left

a95b16cb

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Ken Lee, Chris Hughes
-
-! This file was ported from Lean 3 source module ring_theory.coprime.basic
-! leanprover-community/mathlib commit a95b16cbade0f938fc24abd05412bde1e84bab9b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Tactic.Ring
 import Mathlib.GroupTheory.GroupAction.Units
@@ -14,6 +9,8 @@ import Mathlib.Algebra.Ring.Divisibility
 import Mathlib.Algebra.Hom.Ring
 import Mathlib.Algebra.GroupPower.Ring
 
+#align_import ring_theory.coprime.basic from "leanprover-community/mathlib"@"a95b16cbade0f938fc24abd05412bde1e84bab9b"
+
 /-!
 # Coprime elements of a ring

a95b16cb

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -112,7 +112,7 @@ theorem IsCoprime.mul_left (H1 : IsCoprime x z) (H2 : IsCoprime y z) : IsCoprime
 #align is_coprime.mul_left IsCoprime.mul_left
 
 theorem IsCoprime.mul_right (H1 : IsCoprime x y) (H2 : IsCoprime x z) : IsCoprime x (y * z) := by
-  rw [isCoprime_comm] at H1 H2⊢
+  rw [isCoprime_comm] at H1 H2 ⊢
   exact H1.mul_left H2
 #align is_coprime.mul_right IsCoprime.mul_right
 
@@ -137,7 +137,7 @@ theorem IsCoprime.of_mul_left_right (H : IsCoprime (x * y) z) : IsCoprime y z :=
 #align is_coprime.of_mul_left_right IsCoprime.of_mul_left_right
 
 theorem IsCoprime.of_mul_right_left (H : IsCoprime x (y * z)) : IsCoprime x y := by
-  rw [isCoprime_comm] at H⊢
+  rw [isCoprime_comm] at H ⊢
   exact H.of_mul_left_left
 #align is_coprime.of_mul_right_left IsCoprime.of_mul_right_left
 
@@ -192,7 +192,7 @@ theorem IsCoprime.of_add_mul_right_left (h : IsCoprime (x + z * y) y) : IsCoprim
 #align is_coprime.of_add_mul_right_left IsCoprime.of_add_mul_right_left
 
 theorem IsCoprime.of_add_mul_left_right (h : IsCoprime x (y + x * z)) : IsCoprime x y := by
-  rw [isCoprime_comm] at h⊢
+  rw [isCoprime_comm] at h ⊢
   exact h.of_add_mul_left_left
 #align is_coprime.of_add_mul_left_right IsCoprime.of_add_mul_left_right

a95b16cb

feat: porting norm_num extensions for Nat.gcd, Nat.lcm, Int.gcd, Int.lcm, and IsCoprime (#3923)

This completes the porting of these norm_num extensions while adding a new extension for IsCoprime over Int. It also adds the norm_num extension testing file from mathlib3. Closes #3246.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

c0f7bfde

Diff

@@ -38,7 +38,6 @@ variable {R : Type u} [CommSemiring R] (x y z : R)
 /-- The proposition that `x` and `y` are coprime, defined to be the existence of `a` and `b` such
 that `a * x + b * y = 1`. Note that elements with no common divisors are not necessarily coprime,
 e.g., the multivariate polynomials `x₁` and `x₂` are not coprime. -/
-@[simp]
 def IsCoprime : Prop :=
   ∃ a b, a * x + b * y = 1
 #align is_coprime IsCoprime

a95b16cb

chore: fix more casing errors per naming scheme (#1232)

I've avoided anything under Tactic or test.

In correcting the names, I found Option.isNone_iff_eq_none duplicated between Std and Mathlib, so the Mathlib one has been removed.

Co-authored-by: Reid Barton <rwbarton@gmail.com>

31a56f75

Diff

@@ -74,7 +74,7 @@ theorem not_isCoprime_zero_zero [Nontrivial R] : ¬IsCoprime (0 : R) 0 :=
   mt isCoprime_zero_right.mp not_isUnit_zero
 #align not_coprime_zero_zero not_isCoprime_zero_zero
 
-/-- If a 2-vector `p` satisfies `is_coprime (p 0) (p 1)`, then `p ≠ 0`. -/
+/-- If a 2-vector `p` satisfies `IsCoprime (p 0) (p 1)`, then `p ≠ 0`. -/
 theorem IsCoprime.ne_zero [Nontrivial R] {p : Fin 2 → R} (h : IsCoprime (p 0) (p 1)) : p ≠ 0 := by
   rintro rfl
   exact not_isCoprime_zero_zero h

a95b16cb

chore: fix casing per naming scheme (#1183)

Fix a lot of wrong casing mostly in the docstrings but also sometimes in def/theorem names. E.g. fin 2 --> Fin 2, add_monoid_hom --> AddMonoidHom

Remove \n from to_additive docstrings that were inserted by mathport.

Move files and directories with Gcd and Smul to GCD and SMul

71723d8b

Diff

@@ -164,15 +164,15 @@ theorem IsCoprime.of_isCoprime_of_dvd_right (h : IsCoprime z y) (hdvd : x ∣ y)
   (h.symm.of_isCoprime_of_dvd_left hdvd).symm
 #align is_coprime.of_coprime_of_dvd_right IsCoprime.of_isCoprime_of_dvd_right
 
-theorem IsCoprime.is_unit_of_dvd (H : IsCoprime x y) (d : x ∣ y) : IsUnit x :=
+theorem IsCoprime.isUnit_of_dvd (H : IsCoprime x y) (d : x ∣ y) : IsUnit x :=
   let ⟨k, hk⟩ := d
   isCoprime_self.1 <| IsCoprime.of_mul_right_left <| show IsCoprime x (x * k) from hk ▸ H
-#align is_coprime.is_unit_of_dvd IsCoprime.is_unit_of_dvd
+#align is_coprime.is_unit_of_dvd IsCoprime.isUnit_of_dvd
 
-theorem IsCoprime.is_unit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a) (hb : x ∣ b) :
+theorem IsCoprime.isUnit_of_dvd' {a b x : R} (h : IsCoprime a b) (ha : x ∣ a) (hb : x ∣ b) :
     IsUnit x :=
-  (h.of_isCoprime_of_dvd_left ha).is_unit_of_dvd hb
-#align is_coprime.is_unit_of_dvd' IsCoprime.is_unit_of_dvd'
+  (h.of_isCoprime_of_dvd_left ha).isUnit_of_dvd hb
+#align is_coprime.is_unit_of_dvd' IsCoprime.isUnit_of_dvd'
 
 theorem IsCoprime.map (H : IsCoprime x y) {S : Type v} [CommSemiring S] (f : R →+* S) :
     IsCoprime (f x) (f y) :=

a95b16cb

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

@@ -2,6 +2,11 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Ken Lee, Chris Hughes
+
+! This file was ported from Lean 3 source module ring_theory.coprime.basic
+! leanprover-community/mathlib commit a95b16cbade0f938fc24abd05412bde1e84bab9b
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
 -/
 import Mathlib.Tactic.Ring
 import Mathlib.GroupTheory.GroupAction.Units

`ring_theory.coprime.basic` ⟷ `Mathlib.RingTheory.Coprime.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies

ring_theory.coprime.basic ⟷ Mathlib.RingTheory.Coprime.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies

`ring_theory.coprime.basic` ⟷ `Mathlib.RingTheory.Coprime.Basic`