algebra.monoid_algebra.no_zero_divisors

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

3e067975

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

93287238

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -74,14 +74,14 @@ theorem Left.exists_add_of_mem_support_single_hMul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
   rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _),
-    Finset.mem_map] at hx 
+    Finset.mem_map] at hx
 #align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_hMul
 
 theorem Right.exists_add_of_mem_support_single_hMul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
   rwa [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _),
-    Finset.mem_map] at hx 
+    Finset.mem_map] at hx
 #align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_hMul
 
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right

93287238

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -55,7 +55,17 @@ variable {R A : Type _} [Semiring R]
 as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem hMul_apply_add_eq_hMul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
     (h : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0) :
-    (f * g) (a0 + b0) = f a0 * g b0 := by classical
+    (f * g) (a0 + b0) = f a0 * g b0 := by
+  classical
+  rw [mul_apply]
+  refine' (Finset.sum_eq_single a0 _ _).trans _
+  · exact fun b H hb => Finset.sum_eq_zero fun x H1 => if_neg (h H H1 (Or.inl hb))
+  · exact fun af0 => by simp [not_mem_support_iff.mp af0]
+  · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
+    · by_cases af : a0 ∈ f.support
+      · exact if_neg (h af bg (Or.inr b0))
+      · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
+    · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.hMul_apply_add_eq_hMul_of_forall_ne
 
 section LeftOrRightOrderability

93287238

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -55,17 +55,7 @@ variable {R A : Type _} [Semiring R]
 as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem hMul_apply_add_eq_hMul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
     (h : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0) :
-    (f * g) (a0 + b0) = f a0 * g b0 := by
-  classical
-  rw [mul_apply]
-  refine' (Finset.sum_eq_single a0 _ _).trans _
-  · exact fun b H hb => Finset.sum_eq_zero fun x H1 => if_neg (h H H1 (Or.inl hb))
-  · exact fun af0 => by simp [not_mem_support_iff.mp af0]
-  · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
-    · by_cases af : a0 ∈ f.support
-      · exact if_neg (h af bg (Or.inr b0))
-      · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
-    · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
+    (f * g) (a0 + b0) = f a0 * g b0 := by classical
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.hMul_apply_add_eq_hMul_of_forall_ne
 
 section LeftOrRightOrderability

93287238

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathbin.Algebra.MonoidAlgebra.Support
+import Algebra.MonoidAlgebra.Support
 
 #align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"

93287238

bump to nightly-2023-09-16-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

57ab21b3

Diff

@@ -51,10 +51,9 @@ open Finsupp
 
 variable {R A : Type _} [Semiring R]
 
-#print AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne /-
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
-theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
+theorem hMul_apply_add_eq_hMul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
     (h : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0) :
     (f * g) (a0 + b0) = f a0 * g b0 := by
   classical
@@ -67,30 +66,24 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
       · exact if_neg (h af bg (Or.inr b0))
       · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
     · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
-#align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne
--/
+#align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.hMul_apply_add_eq_hMul_of_forall_ne
 
 section LeftOrRightOrderability
 
-#print AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul /-
-theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
+theorem Left.exists_add_of_mem_support_single_hMul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
   rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _),
     Finset.mem_map] at hx 
-#align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
--/
+#align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_hMul
 
-#print AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul /-
-theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
+theorem Right.exists_add_of_mem_support_single_hMul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
   rwa [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _),
     Finset.mem_map] at hx 
-#align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
--/
+#align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_hMul
 
-#print AddMonoidAlgebra.NoZeroDivisors.of_left_ordered /-
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigroup A]
@@ -128,9 +121,7 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
         · refine' add_lt_add_left _ _
           exact Finset.min'_lt_of_mem_erase_min' _ _ (finset.mem_erase.mpr ⟨hc, cg⟩)⟩
 #align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_ordered
--/
 
-#print AddMonoidAlgebra.NoZeroDivisors.of_right_ordered /-
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a right-ordered add left
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigroup A]
@@ -170,7 +161,6 @@ theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigro
             Add.to_covariantClass_right A
           exact add_le_add_right (Finset.min'_le _ _ bf) _⟩
 #align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_ordered
--/
 
 end LeftOrRightOrderability

93287238

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module algebra.monoid_algebra.no_zero_divisors
-! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.MonoidAlgebra.Support
 
+#align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
 /-!
 # Variations on non-zero divisors in `add_monoid_algebra`s

93287238

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -54,6 +54,7 @@ open Finsupp
 
 variable {R A : Type _} [Semiring R]
 
+#print AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne /-
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
@@ -70,23 +71,29 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
       · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
     · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne
+-/
 
 section LeftOrRightOrderability
 
+#print AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul /-
 theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
   rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _),
     Finset.mem_map] at hx 
 #align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
+-/
 
+#print AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul /-
 theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
   rwa [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _),
     Finset.mem_map] at hx 
 #align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
+-/
 
+#print AddMonoidAlgebra.NoZeroDivisors.of_left_ordered /-
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigroup A]
@@ -124,7 +131,9 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
         · refine' add_lt_add_left _ _
           exact Finset.min'_lt_of_mem_erase_min' _ _ (finset.mem_erase.mpr ⟨hc, cg⟩)⟩
 #align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_ordered
+-/
 
+#print AddMonoidAlgebra.NoZeroDivisors.of_right_ordered /-
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a right-ordered add left
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigroup A]
@@ -164,6 +173,7 @@ theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigro
             Add.to_covariantClass_right A
           exact add_le_add_right (Finset.min'_le _ _ bf) _⟩
 #align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_ordered
+-/
 
 end LeftOrRightOrderability

93287238

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -60,15 +60,15 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
     (h : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0) :
     (f * g) (a0 + b0) = f a0 * g b0 := by
   classical
-    rw [mul_apply]
-    refine' (Finset.sum_eq_single a0 _ _).trans _
-    · exact fun b H hb => Finset.sum_eq_zero fun x H1 => if_neg (h H H1 (Or.inl hb))
-    · exact fun af0 => by simp [not_mem_support_iff.mp af0]
-    · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
-      · by_cases af : a0 ∈ f.support
-        · exact if_neg (h af bg (Or.inr b0))
-        · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
-      · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
+  rw [mul_apply]
+  refine' (Finset.sum_eq_single a0 _ _).trans _
+  · exact fun b H hb => Finset.sum_eq_zero fun x H1 => if_neg (h H H1 (Or.inl hb))
+  · exact fun af0 => by simp [not_mem_support_iff.mp af0]
+  · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
+    · by_cases af : a0 ∈ f.support
+      · exact if_neg (h af bg (Or.inr b0))
+      · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
+    · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne
 
 section LeftOrRightOrderability

93287238

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -77,14 +77,14 @@ theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
   rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _),
-    Finset.mem_map] at hx
+    Finset.mem_map] at hx 
 #align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
 
 theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
   rwa [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _),
-    Finset.mem_map] at hx
+    Finset.mem_map] at hx 
 #align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
 
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
@@ -103,7 +103,7 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
     refine' ⟨a + gmin, mem_support_iff.mpr _⟩
     rw [mul_apply_add_eq_mul_of_forall_ne _]
     · refine' mul_ne_zero _ _
-      exacts[mem_support_iff.mp ha, mem_support_iff.mp (Finset.min'_mem _ _)]
+      exacts [mem_support_iff.mp ha, mem_support_iff.mp (Finset.min'_mem _ _)]
     · rw [H]
       rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
       · refine' lt_of_lt_of_le (_ : _ < b + gmin) _
@@ -142,7 +142,7 @@ theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigro
     refine' ⟨fmin + a, mem_support_iff.mpr _⟩
     rw [mul_apply_add_eq_mul_of_forall_ne _]
     · refine' mul_ne_zero _ _
-      exacts[mem_support_iff.mp (Finset.min'_mem _ _), mem_support_iff.mp ha]
+      exacts [mem_support_iff.mp (Finset.min'_mem _ _), mem_support_iff.mp ha]
     · rw [H]
       rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
       · refine' lt_of_le_of_lt (_ : _ ≤ fmin + c) _

93287238

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -54,12 +54,6 @@ open Finsupp
 
 variable {R A : Type _} [Semiring R]
 
-/- warning: add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne -> AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne is a dubious translation:
-lean 3 declaration is
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 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
@@ -79,12 +73,6 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
 
 section LeftOrRightOrderability
 
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 theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
@@ -92,12 +80,6 @@ theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     Finset.mem_map] at hx
 #align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
 
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 theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
@@ -105,12 +87,6 @@ theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     Finset.mem_map] at hx
 #align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
 
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-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddRightCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))) (LT.lt.{u2} A (Preorder.toHasLt.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
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-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddRightCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
-Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_orderedₓ'. -/
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigroup A]
@@ -149,12 +125,6 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
           exact Finset.min'_lt_of_mem_erase_min' _ _ (finset.mem_erase.mpr ⟨hc, cg⟩)⟩
 #align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_ordered
 
-/- warning: add_monoid_algebra.no_zero_divisors.of_right_ordered -> AddMonoidAlgebra.NoZeroDivisors.of_right_ordered is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddLeftCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (Function.swap.{succ u2, succ u2, succ u2} A A (fun (ᾰ : A) (ᾰ : A) => A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))))) (LT.lt.{u2} A (Preorder.toHasLt.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddLeftCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (Function.swap.{succ u1, succ u1, succ u1} A A (fun (ᾰ : A) (ᾰ : A) => A) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206)) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
-Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_orderedₓ'. -/
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a right-ordered add left
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigroup A]

93287238

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -107,7 +107,7 @@ theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
 
 /- warning: add_monoid_algebra.no_zero_divisors.of_left_ordered -> AddMonoidAlgebra.NoZeroDivisors.of_left_ordered is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddRightCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))) (LT.lt.{u2} A (Preorder.toLT.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddRightCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))) (LT.lt.{u2} A (Preorder.toHasLt.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddRightCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
 Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_orderedₓ'. -/
@@ -151,7 +151,7 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
 
 /- warning: add_monoid_algebra.no_zero_divisors.of_right_ordered -> AddMonoidAlgebra.NoZeroDivisors.of_right_ordered is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddLeftCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (Function.swap.{succ u2, succ u2, succ u2} A A (fun (ᾰ : A) (ᾰ : A) => A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))))) (LT.lt.{u2} A (Preorder.toLT.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddLeftCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (Function.swap.{succ u2, succ u2, succ u2} A A (fun (ᾰ : A) (ᾰ : A) => A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))))) (LT.lt.{u2} A (Preorder.toHasLt.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddLeftCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (Function.swap.{succ u1, succ u1, succ u1} A A (fun (ᾰ : A) (ᾰ : A) => A) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206)) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
 Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_orderedₓ'. -/

93287238

bump to nightly-2023-03-19-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

b19efad4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 
 ! This file was ported from Lean 3 source module algebra.monoid_algebra.no_zero_divisors
-! leanprover-community/mathlib commit 3e067975886cf5801e597925328c335609511b1a
+! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Algebra.MonoidAlgebra.Support
 /-!
 # Variations on non-zero divisors in `add_monoid_algebra`s
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file studies the interaction between typeclass assumptions on two Types `R` and `A` and
 whether `add_monoid_algebra R A` has non-zero zero-divisors.  For some background on related
 questions, see [Kaplansky's Conjectures](https://en.wikipedia.org/wiki/Kaplansky%27s_conjectures),

3e067975

bump to nightly-2023-03-17-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

2bedb1b6

Diff

@@ -51,6 +51,12 @@ open Finsupp
 
 variable {R A : Type _} [Semiring R]
 
+/- warning: add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne -> AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Add.{u2} A] {f : AddMonoidAlgebra.{u1, u2} R A _inst_1} {g : AddMonoidAlgebra.{u1, u2} R A _inst_1} {a0 : A} {b0 : A}, (forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) a (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) f)) -> (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) b (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) g)) -> (Or (Ne.{succ u2} A a a0) (Ne.{succ u2} A b b0)) -> (Ne.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a b) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a0 b0))) -> (Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (fun (_x : AddMonoidAlgebra.{u1, u2} R A _inst_1) => A -> R) (AddMonoidAlgebra.coeFun.{u1, u2} R A _inst_1) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 _inst_2)) f g) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a0 b0)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (fun (_x : AddMonoidAlgebra.{u1, u2} R A _inst_1) => A -> R) (AddMonoidAlgebra.coeFun.{u1, u2} R A _inst_1) f a0) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (fun (_x : AddMonoidAlgebra.{u1, u2} R A _inst_1) => A -> R) (AddMonoidAlgebra.coeFun.{u1, u2} R A _inst_1) g b0)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Add.{u2} A] {f : AddMonoidAlgebra.{u1, u2} R A _inst_1} {g : AddMonoidAlgebra.{u1, u2} R A _inst_1} {a0 : A} {b0 : A}, (forall {a : A} {b : A}, (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) a (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) f)) -> (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) b (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) g)) -> (Or (Ne.{succ u2} A a a0) (Ne.{succ u2} A b b0)) -> (Ne.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a b) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a0 b0))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a0 b0)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Finsupp.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) _x) (Finsupp.funLike.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u1 u2} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 _inst_2)) f g) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A _inst_2) a0 b0)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) b0) ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) (instHMul.{u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) a0) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Finsupp.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) _x) (Finsupp.funLike.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) f a0) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Finsupp.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) A (fun (_x : A) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : A) => R) _x) (Finsupp.funLike.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) g b0)))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_neₓ'. -/
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
@@ -70,6 +76,12 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
 
 section LeftOrRightOrderability
 
+/- warning: add_monoid_algebra.left.exists_add_of_mem_support_single_mul -> AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddLeftCancelSemigroup.{u2} A] {g : AddMonoidAlgebra.{u1, u2} R A _inst_1} (a : A) (x : A), (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) x (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_2)))) (Finsupp.single.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) g))) -> (Exists.{succ u2} A (fun (b : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) b (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) g)) (fun (H : Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) b (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) g)) => Eq.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_2))) a b) x)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddLeftCancelSemigroup.{u2} A] {g : AddMonoidAlgebra.{u1, u2} R A _inst_1} (a : A) (x : A), (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{max u2 u1, max u1 u2, max u1 u2} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_2)))) (AddMonoidAlgebra.single.{u1, u2} R A _inst_1 a (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) g))) -> (Exists.{succ u2} A (fun (b : A) => And (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) b (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) g)) (Eq.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_2))) a b) x)))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mulₓ'. -/
 theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     {g : AddMonoidAlgebra R A} (a x : A)
     (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
@@ -77,6 +89,12 @@ theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
     Finset.mem_map] at hx
 #align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
 
+/- warning: add_monoid_algebra.right.exists_add_of_mem_support_single_mul -> AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddRightCancelSemigroup.{u2} A] {f : AddMonoidAlgebra.{u1, u2} R A _inst_1} (b : A) (x : A), (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) x (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_2)))) f (Finsupp.single.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) b (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))))) -> (Exists.{succ u2} A (fun (a : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) a (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) f)) (fun (H : Membership.Mem.{u2, u2} A (Finset.{u2} A) (Finset.hasMem.{u2} A) a (Finsupp.support.{u2, u1} A R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) f)) => Eq.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_2))) a b) x)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddRightCancelSemigroup.{u2} A] {f : AddMonoidAlgebra.{u1, u2} R A _inst_1} (b : A) (x : A), (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) x (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (HMul.hMul.{max u1 u2, max u2 u1, max u1 u2} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.{u1, u2} R A _inst_1) (instHMul.{max u1 u2} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_2)))) f (AddMonoidAlgebra.single.{u1, u2} R A _inst_1 b (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))))) -> (Exists.{succ u2} A (fun (a : A) => And (Membership.mem.{u2, u2} A (Finset.{u2} A) (Finset.instMembershipFinset.{u2} A) a (Finsupp.support.{u2, u1} A R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) f)) (Eq.{succ u2} A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_2))) a b) x)))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mulₓ'. -/
 theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     {f : AddMonoidAlgebra R A} (b x : A)
     (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
@@ -84,6 +102,12 @@ theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
     Finset.mem_map] at hx
 #align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
 
+/- warning: add_monoid_algebra.no_zero_divisors.of_left_ordered -> AddMonoidAlgebra.NoZeroDivisors.of_left_ordered is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddRightCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))) (LT.lt.{u2} A (Preorder.toLT.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddRightCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddRightCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.587 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.589) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.602 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.604)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddRightCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_orderedₓ'. -/
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigroup A]
@@ -122,6 +146,12 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
           exact Finset.min'_lt_of_mem_erase_min' _ _ (finset.mem_erase.mpr ⟨hc, cg⟩)⟩
 #align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_ordered
 
+/- warning: add_monoid_algebra.no_zero_divisors.of_right_ordered -> AddMonoidAlgebra.NoZeroDivisors.of_right_ordered is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))] [_inst_3 : AddLeftCancelSemigroup.{u2} A] [_inst_4 : LinearOrder.{u2} A] [_inst_5 : CovariantClass.{u2, u2} A A (Function.swap.{succ u2, succ u2, succ u2} A A (fun (ᾰ : A) (ᾰ : A) => A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))))) (LT.lt.{u2} A (Preorder.toLT.{u2} A (PartialOrder.toPreorder.{u2} A (SemilatticeInf.toPartialOrder.{u2} A (Lattice.toSemilatticeInf.{u2} A (LinearOrder.toLattice.{u2} A _inst_4))))))], NoZeroDivisors.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.hasMul.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3))) (MulZeroClass.toHasZero.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (AddMonoidAlgebra.{u1, u2} R A _inst_1) (AddMonoidAlgebra.nonUnitalNonAssocSemiring.{u1, u2} R A _inst_1 (AddSemigroup.toHasAdd.{u2} A (AddLeftCancelSemigroup.toAddSemigroup.{u2} A _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : NoZeroDivisors.{u2} R (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))] [_inst_3 : AddLeftCancelSemigroup.{u1} A] [_inst_4 : LinearOrder.{u1} A] [_inst_5 : CovariantClass.{u1, u1} A A (Function.swap.{succ u1, succ u1, succ u1} A A (fun (ᾰ : A) (ᾰ : A) => A) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206 : A) => HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1204 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1206)) (fun (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 : A) (x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221 : A) => LT.lt.{u1} A (Preorder.toLT.{u1} A (PartialOrder.toPreorder.{u1} A (SemilatticeInf.toPartialOrder.{u1} A (Lattice.toSemilatticeInf.{u1} A (DistribLattice.toLattice.{u1} A (instDistribLattice.{u1} A _inst_4)))))) x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1219 x._@.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors._hyg.1221)], NoZeroDivisors.{max u1 u2} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.hasMul.{u2, u1} R A _inst_1 (AddSemigroup.toAdd.{u1} A (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))) (SemigroupWithZero.toZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (NonUnitalSemiring.toSemigroupWithZero.{max u2 u1} (AddMonoidAlgebra.{u2, u1} R A _inst_1) (AddMonoidAlgebra.nonUnitalSemiring.{u2, u1} R A _inst_1 (AddLeftCancelSemigroup.toAddSemigroup.{u1} A _inst_3))))
+Case conversion may be inaccurate. Consider using '#align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_orderedₓ'. -/
 /-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a right-ordered add left
 cancel semigroup, then `add_monoid_algebra R A` also contains no non-zero zero-divisors. -/
 theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigroup A]

3e067975

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -64,7 +64,7 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
     · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
       · by_cases af : a0 ∈ f.support
         · exact if_neg (h af bg (Or.inr b0))
-        · simp only [not_mem_support_iff.mp af, zero_mul, if_t_t]
+        · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, if_t_t]
       · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne

3e067975

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

3e067975

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathlib.Algebra.MonoidAlgebra.Support
+import Mathlib.Algebra.MonoidAlgebra.Basic
 import Mathlib.Algebra.Group.UniqueProds
 
 #align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"3e067975886cf5801e597925328c335609511b1a"

3e067975

chore: tidy various files (#8409)

f5f44c59

Diff

@@ -97,9 +97,9 @@ as a product of monomials in the supports of `f` and `g` is a product. -/
 theorem mul_apply_add_eq_mul_of_uniqueAdd [Add A] {f g : R[A]} {a0 b0 : A}
     (h : UniqueAdd f.support g.support a0 b0) :
     (f * g) (a0 + b0) = f a0 * g b0 :=
-MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul (A := Multiplicative A) h
+  MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul (A := Multiplicative A) h
 
 instance [NoZeroDivisors R] [Add A] [UniqueSums A] : NoZeroDivisors R[A] :=
-MonoidAlgebra.instNoZeroDivisorsOfUniqueProds (A := Multiplicative A)
+  MonoidAlgebra.instNoZeroDivisorsOfUniqueProds (A := Multiplicative A)
 
 end AddMonoidAlgebra

3e067975

feat: TwoUniqueProds (#7169)

Introduce TwoUniqueProds/Sums: let R[G] be a monoid algebra over a semiring R without zero-divisors. A natural sufficient condition for R[G] to have no zero-divisors is that G has UniqueProds, as is shown by MonoidAlgebra.instNoZeroDivisorsOfUniqueProds. Similarly, a natural sufficient condition for R[G] to have only trivial units (of the form rg with r a unit in R and g a unit in G) is that G has TwoUniqueProds, but we don't prove this yet in this PR. TwoUniqueProds G is also a natural sufficient condition in order for factors of a homogeneous element in an algebra graded by G without zero-divisors to themselves be homogeneous.
Show TwoUniqueProds implies UniqueProds: TwoUniqueProds.toUniqueProds
Strengthen of_Covariant_right/left to have TwoUniqueProds as conclusion
Extract of_image_filter from the proof of the instance UniqueProds (∀ i, G i) and use it also in the proof of TwoUniqueProds (∀ i, G i)
Use some private defs (starting from private abbrev I) to transfer (Two)UniqueProds (∀ i, G i) instances to (Two)UniqueProds (G × H)
Move the [Module ℚ G] : UniqueSums G instance from NoZeroDivisors.lean to UniqueProds.lean and strengthen to TwoUniqueSums

New lemmas about UniqueMul:

of_card_le_one, iff_card_le_one, UniqueMul_of_TwoUniqueMul

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

86fa7890

Diff

@@ -5,7 +5,6 @@ Authors: Damiano Testa
 -/
 import Mathlib.Algebra.MonoidAlgebra.Support
 import Mathlib.Algebra.Group.UniqueProds
-import Mathlib.LinearAlgebra.Basis.VectorSpace
 
 #align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"3e067975886cf5801e597925328c335609511b1a"
 
@@ -104,11 +103,3 @@ instance [NoZeroDivisors R] [Add A] [UniqueSums A] : NoZeroDivisors R[A] :=
 MonoidAlgebra.instNoZeroDivisorsOfUniqueProds (A := Multiplicative A)
 
 end AddMonoidAlgebra
-
-/-- The proof goes via the equivalence `A ≃ₗ[ℚ] (Basis.ofVectorSpaceIndex ℚ A) →₀ ℚ`,
-i.e. choosing a basis.
-Once we have a basis, we use the embedding into sequences of coordinates and all the instances
-that `ℚ` already has.
--/
-instance [AddCommGroup A] [Module ℚ A] : UniqueSums A :=
-  UniqueSums.addHom_image_of_injective _ (Basis.ofVectorSpace ℚ A).repr.injective inferInstance

3e067975

feat(AddMonoidAlgebra*): add notation R[A] for addMonoidAlgebra R A (#7203)

Introduce the notation R[A] for AddMonoidAlgebra R A. This is to align Mathlibs notation with the standard notation for group ring.

The notation is scoped in AddMonoidAlgebra and there is no analogous notation for MonoidAlgebra.

I only used the notation for single-character R and As and only in the range [a-zA-Z].

The extra lines are all in Mathlib/Algebra/MonoidAlgebra/Basic.lean. They are accounted for by extra text in the doc-module and the actual notation.

Affected files:

Counterexamples/ZeroDivisorsInAddMonoidAlgebras
Algebra/AlgebraicCard
Algebra/MonoidAlgebra/Basic
Algebra/MonoidAlgebra/Degree
Algebra/MonoidAlgebra/Division
Algebra/MonoidAlgebra/Grading
Algebra/MonoidAlgebra/NoZeroDivisors
Algebra/MonoidAlgebra/Support
Data/Polynomial/AlgebraMap
Data/Polynomial/Basic
Data/Polynomial/Eval
Data/Polynomial/Laurent
RingTheory/FiniteType

2f19a6b1

Diff

@@ -13,7 +13,7 @@ import Mathlib.LinearAlgebra.Basis.VectorSpace
 # Variations on non-zero divisors in `AddMonoidAlgebra`s
 
 This file studies the interaction between typeclass assumptions on two Types `R` and `A` and
-whether `AddMonoidAlgebra R A` has non-zero zero-divisors.  For some background on related
+whether `R[A]` has non-zero zero-divisors.  For some background on related
 questions, see [Kaplansky's Conjectures](https://en.wikipedia.org/wiki/Kaplansky%27s_conjectures),
 especially the *zero divisor conjecture*.
 
@@ -22,7 +22,7 @@ Let `K` be a field, and `G` a torsion-free group. The group ring `K[G]` does not
 nontrivial zero divisors, that is, it is a domain.
 
 In this file we show that if `R` satisfies `NoZeroDivisors` and `A` is a grading type satisfying
-`UniqueProds A` (resp. `UniqueSums A`), then `MonoidAlgebra R A` (resp. `AddMonoidAlgebra R A`)
+`UniqueProds A` (resp. `UniqueSums A`), then `MonoidAlgebra R A` (resp. `R[A]`)
 also satisfies `NoZeroDivisors`.
 
 Because of the instances to `UniqueProds/Sums`, we obtain a formalization of the well-known result
@@ -39,15 +39,15 @@ The actual assumptions on `R` are weaker.
 * The instance showing that `Semiring R, NoZeroDivisors R, Mul A, UniqueProds A` imply
   `NoZeroDivisors (MonoidAlgebra R A)`.
 * The instance showing that `Semiring R, NoZeroDivisors R, Add A, UniqueSums A` imply
-  `NoZeroDivisors (AddMonoidAlgebra R A)`.
+  `NoZeroDivisors R[A]`.
 
 TODO: move the rest of the docs to UniqueProds?
  `NoZeroDivisors.of_left_ordered` shows that if `R` is a semiring with no non-zero
   zero-divisors, `A` is a linearly ordered, add right cancel semigroup with strictly monotone
-  left addition, then `AddMonoidAlgebra R A` has no non-zero zero-divisors.
+  left addition, then `R[A]` has no non-zero zero-divisors.
 * `NoZeroDivisors.of_right_ordered` shows that if `R` is a semiring with no non-zero
   zero-divisors, `A` is a linearly ordered, add left cancel semigroup with strictly monotone
-  right addition, then `AddMonoidAlgebra R A` has no non-zero zero-divisors.
+  right addition, then `R[A]` has no non-zero zero-divisors.
 
 The conditions on `A` imposed in `NoZeroDivisors.of_left_ordered` are sometimes referred to as
 `left-ordered`.
@@ -95,12 +95,12 @@ namespace AddMonoidAlgebra
 
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
-theorem mul_apply_add_eq_mul_of_uniqueAdd [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
+theorem mul_apply_add_eq_mul_of_uniqueAdd [Add A] {f g : R[A]} {a0 b0 : A}
     (h : UniqueAdd f.support g.support a0 b0) :
     (f * g) (a0 + b0) = f a0 * g b0 :=
 MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul (A := Multiplicative A) h
 
-instance [NoZeroDivisors R] [Add A] [UniqueSums A] : NoZeroDivisors (AddMonoidAlgebra R A) :=
+instance [NoZeroDivisors R] [Add A] [UniqueSums A] : NoZeroDivisors R[A] :=
 MonoidAlgebra.instNoZeroDivisorsOfUniqueProds (A := Multiplicative A)
 
 end AddMonoidAlgebra

3e067975

feat(UniqueProds + NoZeroDivisors): AddMonoidAlgebra instances (#6723)

Add UniqueProds/Sums and NoZeroDivisors instances.

This has recently been prompted by the port of the Lindemann-Weierstrass Theorem, but the results are self-contained. Instances such as the ones in this PR are the reasons why UniqueProds/Sums were introduced.

Affected files:

Algebra/
	Group/UniqueProds.lean
	MonoidAlgebra/NoZeroDivisors.lean

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

96d78537

Diff

@@ -4,6 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
 import Mathlib.Algebra.MonoidAlgebra.Support
+import Mathlib.Algebra.Group.UniqueProds
+import Mathlib.LinearAlgebra.Basis.VectorSpace
 
 #align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"3e067975886cf5801e597925328c335609511b1a"
 
@@ -19,13 +21,28 @@ _Conjecture._
 Let `K` be a field, and `G` a torsion-free group. The group ring `K[G]` does not contain
 nontrivial zero divisors, that is, it is a domain.
 
-We formalize in this file the well-known result that if `R` is a field and `A` is a left-ordered
-group, then `R[A]` contains no non-zero zero-divisors.  Some of these assumptions can be trivially
-weakened: below we mention what assumptions are sufficient for the proofs in this file.
+In this file we show that if `R` satisfies `NoZeroDivisors` and `A` is a grading type satisfying
+`UniqueProds A` (resp. `UniqueSums A`), then `MonoidAlgebra R A` (resp. `AddMonoidAlgebra R A`)
+also satisfies `NoZeroDivisors`.
+
+Because of the instances to `UniqueProds/Sums`, we obtain a formalization of the well-known result
+that if `R` is a field and `A` is a left-ordered group, then `R[A]` contains no non-zero
+zero-divisors.
+The actual assumptions on `R` are weaker.
 
 ##  Main results
 
-* `NoZeroDivisors.of_left_ordered` shows that if `R` is a semiring with no non-zero
+* `MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul` and
+  `AddMonoidAlgebra.mul_apply_add_eq_mul_of_uniqueAdd`
+  general sufficient results stating that certain monomials in a product have as coefficient a
+  product of coefficients of the factors.
+* The instance showing that `Semiring R, NoZeroDivisors R, Mul A, UniqueProds A` imply
+  `NoZeroDivisors (MonoidAlgebra R A)`.
+* The instance showing that `Semiring R, NoZeroDivisors R, Add A, UniqueSums A` imply
+  `NoZeroDivisors (AddMonoidAlgebra R A)`.
+
+TODO: move the rest of the docs to UniqueProds?
+ `NoZeroDivisors.of_left_ordered` shows that if `R` is a semiring with no non-zero
   zero-divisors, `A` is a linearly ordered, add right cancel semigroup with strictly monotone
   left addition, then `AddMonoidAlgebra R A` has no non-zero zero-divisors.
 * `NoZeroDivisors.of_right_ordered` shows that if `R` is a semiring with no non-zero
@@ -41,124 +58,57 @@ These conditions are sufficient, but not necessary.  As mentioned above, *Kaplan
 asserts that `A` being torsion-free may be enough.
 -/
 
-
-namespace AddMonoidAlgebra
-
 open Finsupp
 
 variable {R A : Type*} [Semiring R]
 
+namespace MonoidAlgebra
+
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/
-theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
-    (h : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0) :
-    (f * g) (a0 + b0) = f a0 * g b0 := by
+theorem mul_apply_mul_eq_mul_of_uniqueMul [Mul A] {f g : MonoidAlgebra R A} {a0 b0 : A}
+    (h : UniqueMul f.support g.support a0 b0) :
+    (f * g) (a0 * b0) = f a0 * g b0 := by
   classical
-    rw [mul_apply]
-    refine' (Finset.sum_eq_single a0 _ _).trans _
-    · exact fun b H hb => Finset.sum_eq_zero fun x H1 => if_neg (h H H1 (Or.inl hb))
-    · exact fun af0 => by simp [not_mem_support_iff.mp af0]
-    · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
-      · by_cases af : a0 ∈ f.support
-        · exact if_neg (h af bg (Or.inr b0))
-        · simp only [not_mem_support_iff.mp af, zero_mul, ite_self]
-      · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
-#align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne
-
-section LeftOrRightOrderability
-
-theorem Left.exists_add_of_mem_support_single_mul [AddLeftCancelSemigroup A]
-    {g : AddMonoidAlgebra R A} (a x : A)
-    (hx : x ∈ (single a 1 * g : AddMonoidAlgebra R A).support) : ∃ b ∈ g.support, a + b = x := by
-  rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _),
-    Finset.mem_map] at hx
-#align add_monoid_algebra.left.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul
-
-theorem Right.exists_add_of_mem_support_single_mul [AddRightCancelSemigroup A]
-    {f : AddMonoidAlgebra R A} (b x : A)
-    (hx : x ∈ (f * single b 1 : AddMonoidAlgebra R A).support) : ∃ a ∈ f.support, a + b = x := by
-  rwa [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _),
-    Finset.mem_map] at hx
-#align add_monoid_algebra.right.exists_add_of_mem_support_single_mul AddMonoidAlgebra.Right.exists_add_of_mem_support_single_mul
-
-/-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a left-ordered add right
-cancel semigroup, then `AddMonoidAlgebra R A` also contains no non-zero zero-divisors. -/
-theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigroup A]
-    [LinearOrder A] [CovariantClass A A (· + ·) (· < ·)] : NoZeroDivisors (AddMonoidAlgebra R A) :=
-  ⟨@fun f g fg => by
-    contrapose! fg
-    let gmin : A := g.support.min' (support_nonempty_iff.mpr fg.2)
-    refine' support_nonempty_iff.mp _
-    obtain ⟨a, ha, H⟩ :=
-      Right.exists_add_of_mem_support_single_mul gmin
-        ((f * single gmin 1 : AddMonoidAlgebra R A).support.min'
-          (by rw [support_mul_single] <;> simp [support_nonempty_iff.mpr fg.1]))
-        (Finset.min'_mem _ _)
-    refine' ⟨a + gmin, mem_support_iff.mpr _⟩
-    rw [mul_apply_add_eq_mul_of_forall_ne _]
-    · refine' mul_ne_zero _ _
-      exacts [mem_support_iff.mp ha, mem_support_iff.mp (Finset.min'_mem _ _)]
-    · rw [H]
-      rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
-      · refine' lt_of_lt_of_le (_ : _ < b + gmin) _
-        · apply Finset.min'_lt_of_mem_erase_min'
-          rw [← H]
-          apply Finset.mem_erase_of_ne_of_mem
-          · simpa only [Ne.def, add_left_inj]
-          · rw [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _)]
-            simpa only [Finset.mem_map, addRightEmbedding_apply, add_left_inj, exists_prop,
-              exists_eq_right]
-        · haveI : CovariantClass A A (· + ·) (· ≤ ·) := covariantClass_le_of_lt A A _
-          exact add_le_add_left (Finset.min'_le _ _ cg) _
-      · refine' lt_of_le_of_lt (_ : _ ≤ b + gmin) _
-        · apply Finset.min'_le
-          rw [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _)]
-          simp only [bf, Finset.mem_map, addRightEmbedding_apply, add_left_inj, exists_prop,
-            exists_eq_right]
-        · refine' add_lt_add_left _ _
-          exact Finset.min'_lt_of_mem_erase_min' _ _ (Finset.mem_erase.mpr ⟨hc, cg⟩)⟩
-#align add_monoid_algebra.no_zero_divisors.of_left_ordered AddMonoidAlgebra.NoZeroDivisors.of_left_ordered
-
-/-- If `R` is a semiring with no non-trivial zero-divisors and `A` is a right-ordered add left
-cancel semigroup, then `AddMonoidAlgebra R A` also contains no non-zero zero-divisors. -/
-theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigroup A]
-    [LinearOrder A] [CovariantClass A A (Function.swap (· + ·)) (· < ·)] :
-    NoZeroDivisors (AddMonoidAlgebra R A) :=
-  ⟨@fun f g fg => by
-    contrapose! fg
-    let fmin : A := f.support.min' (support_nonempty_iff.mpr fg.1)
-    refine' support_nonempty_iff.mp _
-    obtain ⟨a, ha, H⟩ :=
-      Left.exists_add_of_mem_support_single_mul fmin
-        ((single fmin 1 * g : AddMonoidAlgebra R A).support.min'
-          (by rw [support_single_mul] <;> simp [support_nonempty_iff.mpr fg.2]))
-        (Finset.min'_mem _ _)
-    refine' ⟨fmin + a, mem_support_iff.mpr _⟩
-    rw [mul_apply_add_eq_mul_of_forall_ne _]
-    · refine' mul_ne_zero _ _
-      exacts [mem_support_iff.mp (Finset.min'_mem _ _), mem_support_iff.mp ha]
-    · rw [H]
-      rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
-      · refine' lt_of_le_of_lt (_ : _ ≤ fmin + c) _
-        · apply Finset.min'_le
-          rw [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _)]
-          simp only [cg, Finset.mem_map, addLeftEmbedding_apply, add_right_inj, exists_prop,
-            exists_eq_right]
-        · refine' add_lt_add_right _ _
-          exact Finset.min'_lt_of_mem_erase_min' _ _ (Finset.mem_erase.mpr ⟨hb, bf⟩)
-      · refine' lt_of_lt_of_le (_ : _ < fmin + c) _
-        · apply Finset.min'_lt_of_mem_erase_min'
-          rw [← H]
-          apply Finset.mem_erase_of_ne_of_mem
-          · simpa only [Ne.def, add_right_inj]
-          · rw [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y : R, 1 * y = 0 ↔ _)]
-            simpa only [Finset.mem_map, addLeftEmbedding_apply, add_right_inj, exists_prop,
-              exists_eq_right]
-        · haveI : CovariantClass A A (Function.swap (· + ·)) (· ≤ ·) :=
-            covariantClass_le_of_lt A A _
-          exact add_le_add_right (Finset.min'_le _ _ bf) _⟩
-#align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_ordered
-
-end LeftOrRightOrderability
+  simp_rw [mul_apply, sum, ← Finset.sum_product']
+  refine' (Finset.sum_eq_single (a0, b0) _ _).trans (if_pos rfl) <;> simp_rw [Finset.mem_product]
+  · refine fun ab hab hne => if_neg (fun he => hne <| Prod.ext ?_ ?_)
+    exacts [(h hab.1 hab.2 he).1, (h hab.1 hab.2 he).2]
+  · refine fun hnmem => ite_eq_right_iff.mpr (fun _ => ?_)
+    rcases not_and_or.mp hnmem with af | bg
+    · rw [not_mem_support_iff.mp af, zero_mul]
+    · rw [not_mem_support_iff.mp bg, mul_zero]
+
+instance instNoZeroDivisorsOfUniqueProds [NoZeroDivisors R] [Mul A] [UniqueProds A] :
+    NoZeroDivisors (MonoidAlgebra R A) where
+  eq_zero_or_eq_zero_of_mul_eq_zero {a b} ab := by
+    contrapose! ab
+    obtain ⟨da, a0, db, b0, h⟩ := UniqueProds.uniqueMul_of_nonempty
+      (support_nonempty_iff.mpr ab.1) (support_nonempty_iff.mpr ab.2)
+    refine support_nonempty_iff.mp ⟨da * db, ?_⟩
+    rw [mem_support_iff] at a0 b0 ⊢
+    exact mul_apply_mul_eq_mul_of_uniqueMul h ▸ mul_ne_zero a0 b0
+
+end MonoidAlgebra
+
+namespace AddMonoidAlgebra
+
+/-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
+as a product of monomials in the supports of `f` and `g` is a product. -/
+theorem mul_apply_add_eq_mul_of_uniqueAdd [Add A] {f g : AddMonoidAlgebra R A} {a0 b0 : A}
+    (h : UniqueAdd f.support g.support a0 b0) :
+    (f * g) (a0 + b0) = f a0 * g b0 :=
+MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul (A := Multiplicative A) h
+
+instance [NoZeroDivisors R] [Add A] [UniqueSums A] : NoZeroDivisors (AddMonoidAlgebra R A) :=
+MonoidAlgebra.instNoZeroDivisorsOfUniqueProds (A := Multiplicative A)
 
 end AddMonoidAlgebra
+
+/-- The proof goes via the equivalence `A ≃ₗ[ℚ] (Basis.ofVectorSpaceIndex ℚ A) →₀ ℚ`,
+i.e. choosing a basis.
+Once we have a basis, we use the embedding into sequences of coordinates and all the instances
+that `ℚ` already has.
+-/
+instance [AddCommGroup A] [Module ℚ A] : UniqueSums A :=
+  UniqueSums.addHom_image_of_injective _ (Basis.ofVectorSpace ℚ A).repr.injective inferInstance

3e067975

chore(Co(ntra)variantClass): generalize and remove duplicates (#6677)

4 files have major changes:

Algebra/CovariantAndContravariant.lean

Add new theorem contravariant_le_iff_contravariant_lt_and_eq.
Add covariantClass_le_of_lt generalizing and replacing Mul.to_covariantClass_left/right in Algebra/Order/Monoid/Defs.lean
Replace CommSemigroup by IsSymmOp N N mu and replace CancelSemigroup by IsMulCancel, removing superfluous associativity assumption.
new theorems covariant_lt_of_covariant_le_of_contravariant_eq and contravariant_le_of_contravariant_eq_and_lt that could replace eight instances when appropriate refactoring is in place.
Golfs
Fix changed names in other files.

Algebra/Order/Monoid/Lemmas.lean

Generalize mul_eq_mul_iff_eq_and_eq and remove the less general Left/Right.mul_eq_mul_iff_eq_and_eq.
Move mul_le_mul_iff_of_ge.
Introduce the more general Left/Right versions of min_le_max_of_mul_le_mul.
Move min_lt_max_of_mul_lt_mul here from Algebra/GroupPower/Order.lean.
Replace CommSemigroup by IsSymmOp.

Algebra/Order/Monoid/Basic.lean

Remove eq_and_eq_of_le_of_le_of_mul_le as it's just one direction of mul_le_mul_iff_of_ge but with more assumptions.

Algebra/Order/Ring/Lemmas.lean

Generalize two versions of mul_eq_mul_iff_eq_and_eq_of_pos
Golfs

Changes to Algebra/Group/UniqueProds.lean and Algebra/MonoidAlgebra/NoZeroDivisors.lean are in declarations that will be removed by #6723.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

9476eae9

Diff

@@ -108,7 +108,7 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
           · rw [support_mul_single _ _ (fun y => by rw [mul_one] : ∀ y : R, y * 1 = 0 ↔ _)]
             simpa only [Finset.mem_map, addRightEmbedding_apply, add_left_inj, exists_prop,
               exists_eq_right]
-        · haveI : CovariantClass A A (· + ·) (· ≤ ·) := Add.to_covariantClass_left A
+        · haveI : CovariantClass A A (· + ·) (· ≤ ·) := covariantClass_le_of_lt A A _
           exact add_le_add_left (Finset.min'_le _ _ cg) _
       · refine' lt_of_le_of_lt (_ : _ ≤ b + gmin) _
         · apply Finset.min'_le
@@ -155,7 +155,7 @@ theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigro
             simpa only [Finset.mem_map, addLeftEmbedding_apply, add_right_inj, exists_prop,
               exists_eq_right]
         · haveI : CovariantClass A A (Function.swap (· + ·)) (· ≤ ·) :=
-            Add.to_covariantClass_right A
+            covariantClass_le_of_lt A A _
           exact add_le_add_right (Finset.min'_le _ _ bf) _⟩
 #align add_monoid_algebra.no_zero_divisors.of_right_ordered AddMonoidAlgebra.NoZeroDivisors.of_right_ordered

3e067975

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -61,7 +61,7 @@ theorem mul_apply_add_eq_mul_of_forall_ne [Add A] {f g : AddMonoidAlgebra R A} {
     · refine' (Finset.sum_eq_single b0 (fun b bg b0 => _) _).trans (if_pos rfl)
       · by_cases af : a0 ∈ f.support
         · exact if_neg (h af bg (Or.inr b0))
-        · simp only [not_mem_support_iff.mp af, MulZeroClass.zero_mul, ite_self]
+        · simp only [not_mem_support_iff.mp af, zero_mul, ite_self]
       · exact fun bf0 => by simp [not_mem_support_iff.mp bf0]
 #align add_monoid_algebra.mul_apply_add_eq_mul_of_forall_ne AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne

3e067975

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

@@ -46,7 +46,7 @@ namespace AddMonoidAlgebra
 
 open Finsupp
 
-variable {R A : Type _} [Semiring R]
+variable {R A : Type*} [Semiring R]
 
 /-- The coefficient of a monomial in a product `f * g` that can be reached in at most one way
 as a product of monomials in the supports of `f` and `g` is a product. -/

3e067975

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module algebra.monoid_algebra.no_zero_divisors
-! leanprover-community/mathlib commit 3e067975886cf5801e597925328c335609511b1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.MonoidAlgebra.Support
 
+#align_import algebra.monoid_algebra.no_zero_divisors from "leanprover-community/mathlib"@"3e067975886cf5801e597925328c335609511b1a"
+
 /-!
 # Variations on non-zero divisors in `AddMonoidAlgebra`s

3e067975

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -100,7 +100,7 @@ theorem NoZeroDivisors.of_left_ordered [NoZeroDivisors R] [AddRightCancelSemigro
     refine' ⟨a + gmin, mem_support_iff.mpr _⟩
     rw [mul_apply_add_eq_mul_of_forall_ne _]
     · refine' mul_ne_zero _ _
-      exacts[mem_support_iff.mp ha, mem_support_iff.mp (Finset.min'_mem _ _)]
+      exacts [mem_support_iff.mp ha, mem_support_iff.mp (Finset.min'_mem _ _)]
     · rw [H]
       rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
       · refine' lt_of_lt_of_le (_ : _ < b + gmin) _
@@ -139,7 +139,7 @@ theorem NoZeroDivisors.of_right_ordered [NoZeroDivisors R] [AddLeftCancelSemigro
     refine' ⟨fmin + a, mem_support_iff.mpr _⟩
     rw [mul_apply_add_eq_mul_of_forall_ne _]
     · refine' mul_ne_zero _ _
-      exacts[mem_support_iff.mp (Finset.min'_mem _ _), mem_support_iff.mp ha]
+      exacts [mem_support_iff.mp (Finset.min'_mem _ _), mem_support_iff.mp ha]
     · rw [H]
       rintro b c bf cg (hb | hc) <;> refine' ne_of_gt _
       · refine' lt_of_le_of_lt (_ : _ ≤ fmin + c) _

3e067975

feat: port Algebra.MonoidAlgebra.NoZeroDivisors (#2938)

Co-authored-by: Moritz Firsching <firsching@google.com>

70467354

`algebra.monoid_algebra.no_zero_divisors` ⟷ `Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 377

algebra.monoid_algebra.no_zero_divisors ⟷ Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 377

`algebra.monoid_algebra.no_zero_divisors` ⟷ `Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors`