ring_theory.ideal.prod | 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

052f6013

(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

@@ -156,7 +156,7 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
   by
   constructor
   · rcases h with ⟨h, -⟩; contrapose! h
-    rw [← prod_top_top, Prod.ext_iff] at h 
+    rw [← prod_top_top, Prod.ext_iff] at h
     exact h.1
   rintro ⟨r₁, s₁⟩ ⟨r₂, s₂⟩ ⟨h₁, h₂⟩
   cases' h.mem_or_mem h₁ with h h

93287238

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -179,7 +179,7 @@ theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
     (Ideal.prod I J).IsPrime → I = ⊤ ∨ J = ⊤ :=
   by
   contrapose!
-  simp only [ne_top_iff_one, is_prime_iff, not_and, not_forall, not_or]
+  simp only [ne_top_iff_one, is_prime_iff, not_and, Classical.not_forall, not_or]
   exact fun ⟨hI, hJ⟩ hIJ => ⟨⟨0, 1⟩, ⟨1, 0⟩, by simp, by simp [hJ], by simp [hI]⟩
 #align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_aux
 -/

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) 2020 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
 -/
-import Mathbin.RingTheory.Ideal.Operations
+import RingTheory.Ideal.Operations
 
 #align_import ring_theory.ideal.prod from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"

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) 2020 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module ring_theory.ideal.prod
-! 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.RingTheory.Ideal.Operations
 
+#align_import ring_theory.ideal.prod from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
 /-!
 # Ideals in product rings

93287238

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -29,6 +29,7 @@ variable {R : Type u} {S : Type v} [Ring R] [Ring S] (I I' : Ideal R) (J J' : Id
 
 namespace Ideal
 
+#print Ideal.prod /-
 /-- `I × J` as an ideal of `R × S`. -/
 def prod : Ideal (R × S) where
   carrier := {x | x.fst ∈ I ∧ x.snd ∈ J}
@@ -40,6 +41,7 @@ def prod : Ideal (R × S) where
     rintro ⟨a₁, a₂⟩ ⟨b₁, b₂⟩ ⟨hb₁, hb₂⟩
     exact ⟨I.mul_mem_left _ hb₁, J.mul_mem_left _ hb₂⟩
 #align ideal.prod Ideal.prod
+-/
 
 #print Ideal.mem_prod /-
 @[simp]
@@ -48,11 +50,14 @@ theorem mem_prod {r : R} {s : S} : (⟨r, s⟩ : R × S) ∈ prod I J ↔ r ∈
 #align ideal.mem_prod Ideal.mem_prod
 -/
 
+#print Ideal.prod_top_top /-
 @[simp]
 theorem prod_top_top : prod (⊤ : Ideal R) (⊤ : Ideal S) = ⊤ :=
   Ideal.ext <| by simp
 #align ideal.prod_top_top Ideal.prod_top_top
+-/
 
+#print Ideal.ideal_prod_eq /-
 /-- Every ideal of the product ring is of the form `I × J`, where `I` and `J` can be explicitly
     given as the image under the projection maps. -/
 theorem ideal_prod_eq (I : Ideal (R × S)) :
@@ -66,7 +71,9 @@ theorem ideal_prod_eq (I : Ideal (R × S)) :
   rintro ⟨⟨⟨r, s'⟩, ⟨h₁, rfl⟩⟩, ⟨⟨r', s⟩, ⟨h₂, rfl⟩⟩⟩
   simpa using I.add_mem (I.mul_mem_left (1, 0) h₁) (I.mul_mem_left (0, 1) h₂)
 #align ideal.ideal_prod_eq Ideal.ideal_prod_eq
+-/
 
+#print Ideal.map_fst_prod /-
 @[simp]
 theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I J) = I :=
   by
@@ -74,7 +81,9 @@ theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I
   rw [mem_map_iff_of_surjective (RingHom.fst R S) Prod.fst_surjective]
   exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.1, fun h => ⟨⟨x, 0⟩, ⟨⟨h, Ideal.zero_mem _⟩, rfl⟩⟩⟩
 #align ideal.map_fst_prod Ideal.map_fst_prod
+-/
 
+#print Ideal.map_snd_prod /-
 @[simp]
 theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I J) = J :=
   by
@@ -82,7 +91,9 @@ theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I
   rw [mem_map_iff_of_surjective (RingHom.snd R S) Prod.snd_surjective]
   exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.2, fun h => ⟨⟨0, x⟩, ⟨⟨Ideal.zero_mem _, h⟩, rfl⟩⟩⟩
 #align ideal.map_snd_prod Ideal.map_snd_prod
+-/
 
+#print Ideal.map_prodComm_prod /-
 @[simp]
 theorem map_prodComm_prod :
     map ((RingEquiv.prodComm : R × S ≃+* S × R) : R × S →+* S × R) (prod I J) = prod J I :=
@@ -90,7 +101,9 @@ theorem map_prodComm_prod :
   refine' trans (ideal_prod_eq _) _
   simp [map_map]
 #align ideal.map_prod_comm_prod Ideal.map_prodComm_prod
+-/
 
+#print Ideal.idealProdEquiv /-
 /-- Ideals of `R × S` are in one-to-one correspondence with pairs of ideals of `R` and ideals of
     `S`. -/
 def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
@@ -100,18 +113,24 @@ def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
   left_inv I := (ideal_prod_eq I).symm
   right_inv := fun ⟨I, J⟩ => by simp
 #align ideal.ideal_prod_equiv Ideal.idealProdEquiv
+-/
 
+#print Ideal.idealProdEquiv_symm_apply /-
 @[simp]
 theorem idealProdEquiv_symm_apply (I : Ideal R) (J : Ideal S) :
     idealProdEquiv.symm ⟨I, J⟩ = prod I J :=
   rfl
 #align ideal.ideal_prod_equiv_symm_apply Ideal.idealProdEquiv_symm_apply
+-/
 
+#print Ideal.prod.ext_iff /-
 theorem prod.ext_iff {I I' : Ideal R} {J J' : Ideal S} : prod I J = prod I' J' ↔ I = I' ∧ J = J' :=
   by
   simp only [← ideal_prod_equiv_symm_apply, ideal_prod_equiv.symm.injective.eq_iff, Prod.mk.inj_iff]
 #align ideal.prod.ext_iff Ideal.prod.ext_iff
+-/
 
+#print Ideal.isPrime_of_isPrime_prod_top /-
 theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Ideal S)).IsPrime) :
     I.IsPrime := by
   constructor
@@ -124,14 +143,18 @@ theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Idea
       exact ⟨hxy, trivial⟩
     simpa using h.mem_or_mem this
 #align ideal.is_prime_of_is_prime_prod_top Ideal.isPrime_of_isPrime_prod_top
+-/
 
+#print Ideal.isPrime_of_isPrime_prod_top' /-
 theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal R) I).IsPrime) :
     I.IsPrime := by
   apply @is_prime_of_is_prime_prod_top _ R
   rw [← map_prod_comm_prod]
   exact map_is_prime_of_equiv _
 #align ideal.is_prime_of_is_prime_prod_top' Ideal.isPrime_of_isPrime_prod_top'
+-/
 
+#print Ideal.isPrime_ideal_prod_top /-
 theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Ideal S)).IsPrime :=
   by
   constructor
@@ -143,14 +166,18 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
   · exact Or.inl ⟨h, trivial⟩
   · exact Or.inr ⟨h, trivial⟩
 #align ideal.is_prime_ideal_prod_top Ideal.isPrime_ideal_prod_top
+-/
 
+#print Ideal.isPrime_ideal_prod_top' /-
 theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ideal R) I).IsPrime :=
   by
   rw [← map_prod_comm_prod]
   apply map_is_prime_of_equiv _
   exact is_prime_ideal_prod_top
 #align ideal.is_prime_ideal_prod_top' Ideal.isPrime_ideal_prod_top'
+-/
 
+#print Ideal.ideal_prod_prime_aux /-
 theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
     (Ideal.prod I J).IsPrime → I = ⊤ ∨ J = ⊤ :=
   by
@@ -158,7 +185,9 @@ theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
   simp only [ne_top_iff_one, is_prime_iff, not_and, not_forall, not_or]
   exact fun ⟨hI, hJ⟩ hIJ => ⟨⟨0, 1⟩, ⟨1, 0⟩, by simp, by simp [hJ], by simp [hI]⟩
 #align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_aux
+-/
 
+#print Ideal.ideal_prod_prime /-
 /-- Classification of prime ideals in product rings: the prime ideals of `R × S` are precisely the
     ideals of the form `p × S` or `R × p`, where `p` is a prime ideal of `R` or `S`. -/
 theorem ideal_prod_prime (I : Ideal (R × S)) :
@@ -180,6 +209,7 @@ theorem ideal_prod_prime (I : Ideal (R × S)) :
     · exact is_prime_ideal_prod_top
     · exact is_prime_ideal_prod_top'
 #align ideal.ideal_prod_prime Ideal.ideal_prod_prime
+-/
 
 end Ideal

93287238

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -31,7 +31,7 @@ namespace Ideal
 
 /-- `I × J` as an ideal of `R × S`. -/
 def prod : Ideal (R × S) where
-  carrier := { x | x.fst ∈ I ∧ x.snd ∈ J }
+  carrier := {x | x.fst ∈ I ∧ x.snd ∈ J}
   zero_mem' := by simp
   add_mem' := by
     rintro ⟨a₁, a₂⟩ ⟨b₁, b₂⟩ ⟨ha₁, ha₂⟩ ⟨hb₁, hb₂⟩

93287238

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -136,7 +136,7 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
   by
   constructor
   · rcases h with ⟨h, -⟩; contrapose! h
-    rw [← prod_top_top, Prod.ext_iff] at h
+    rw [← prod_top_top, Prod.ext_iff] at h 
     exact h.1
   rintro ⟨r₁, s₁⟩ ⟨r₂, s₂⟩ ⟨h₁, h₂⟩
   cases' h.mem_or_mem h₁ with h h
@@ -171,10 +171,10 @@ theorem ideal_prod_prime (I : Ideal (R × S)) :
     intro hI
     rcases ideal_prod_prime_aux hI with (h | h)
     · right
-      rw [h] at hI⊢
+      rw [h] at hI ⊢
       exact ⟨_, ⟨is_prime_of_is_prime_prod_top' hI, rfl⟩⟩
     · left
-      rw [h] at hI⊢
+      rw [h] at hI ⊢
       exact ⟨_, ⟨is_prime_of_is_prime_prod_top hI, rfl⟩⟩
   · rintro (⟨p, ⟨h, rfl⟩⟩ | ⟨p, ⟨h, rfl⟩⟩)
     · exact is_prime_ideal_prod_top

93287238

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -29,12 +29,6 @@ variable {R : Type u} {S : Type v} [Ring R] [Ring S] (I I' : Ideal R) (J J' : Id
 
 namespace Ideal
 
-/- warning: ideal.prod -> Ideal.prod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S], (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) -> (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S], (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) -> (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))
-Case conversion may be inaccurate. Consider using '#align ideal.prod Ideal.prodₓ'. -/
 /-- `I × J` as an ideal of `R × S`. -/
 def prod : Ideal (R × S) where
   carrier := { x | x.fst ∈ I ∧ x.snd ∈ J }
@@ -54,23 +48,11 @@ theorem mem_prod {r : R} {s : S} : (⟨r, s⟩ : R × S) ∈ prod I J ↔ r ∈
 #align ideal.mem_prod Ideal.mem_prod
 -/
 
-/- warning: ideal.prod_top_top -> Ideal.prod_top_top is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S], Eq.{succ (max u1 u2)} (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.hasTop.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) (Top.top.{max u1 u2} (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Submodule.hasTop.{max u1 u2, max u1 u2} (Prod.{u1, u2} R S) (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Prod.{u1, u2} R S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Prod.{u1, u2} R S) (Semiring.toNonAssocSemiring.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))))) (Semiring.toModule.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))))
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-Case conversion may be inaccurate. Consider using '#align ideal.prod_top_top Ideal.prod_top_topₓ'. -/
 @[simp]
 theorem prod_top_top : prod (⊤ : Ideal R) (⊤ : Ideal S) = ⊤ :=
   Ideal.ext <| by simp
 #align ideal.prod_top_top Ideal.prod_top_top
 
-/- warning: ideal.ideal_prod_eq -> Ideal.ideal_prod_eq is a dubious translation:
-lean 3 declaration is
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 /-- Every ideal of the product ring is of the form `I × J`, where `I` and `J` can be explicitly
     given as the image under the projection maps. -/
 theorem ideal_prod_eq (I : Ideal (R × S)) :
@@ -85,12 +67,6 @@ theorem ideal_prod_eq (I : Ideal (R × S)) :
   simpa using I.add_mem (I.mul_mem_left (1, 0) h₁) (I.mul_mem_left (0, 1) h₂)
 #align ideal.ideal_prod_eq Ideal.ideal_prod_eq
 
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 @[simp]
 theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I J) = I :=
   by
@@ -99,12 +75,6 @@ theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I
   exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.1, fun h => ⟨⟨x, 0⟩, ⟨⟨h, Ideal.zero_mem _⟩, rfl⟩⟩⟩
 #align ideal.map_fst_prod Ideal.map_fst_prod
 
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 @[simp]
 theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I J) = J :=
   by
@@ -113,9 +83,6 @@ theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I
   exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.2, fun h => ⟨⟨0, x⟩, ⟨⟨Ideal.zero_mem _, h⟩, rfl⟩⟩⟩
 #align ideal.map_snd_prod Ideal.map_snd_prod
 
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 @[simp]
 theorem map_prodComm_prod :
     map ((RingEquiv.prodComm : R × S ≃+* S × R) : R × S →+* S × R) (prod I J) = prod J I :=
@@ -124,12 +91,6 @@ theorem map_prodComm_prod :
   simp [map_map]
 #align ideal.map_prod_comm_prod Ideal.map_prodComm_prod
 
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 /-- Ideals of `R × S` are in one-to-one correspondence with pairs of ideals of `R` and ideals of
     `S`. -/
 def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
@@ -140,35 +101,17 @@ def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
   right_inv := fun ⟨I, J⟩ => by simp
 #align ideal.ideal_prod_equiv Ideal.idealProdEquiv
 
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 @[simp]
 theorem idealProdEquiv_symm_apply (I : Ideal R) (J : Ideal S) :
     idealProdEquiv.symm ⟨I, J⟩ = prod I J :=
   rfl
 #align ideal.ideal_prod_equiv_symm_apply Ideal.idealProdEquiv_symm_apply
 
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 theorem prod.ext_iff {I I' : Ideal R} {J J' : Ideal S} : prod I J = prod I' J' ↔ I = I' ∧ J = J' :=
   by
   simp only [← ideal_prod_equiv_symm_apply, ideal_prod_equiv.symm.injective.eq_iff, Prod.mk.inj_iff]
 #align ideal.prod.ext_iff Ideal.prod.ext_iff
 
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 theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Ideal S)).IsPrime) :
     I.IsPrime := by
   constructor
@@ -182,12 +125,6 @@ theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Idea
     simpa using h.mem_or_mem this
 #align ideal.is_prime_of_is_prime_prod_top Ideal.isPrime_of_isPrime_prod_top
 
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 theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal R) I).IsPrime) :
     I.IsPrime := by
   apply @is_prime_of_is_prime_prod_top _ R
@@ -195,12 +132,6 @@ theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal
   exact map_is_prime_of_equiv _
 #align ideal.is_prime_of_is_prime_prod_top' Ideal.isPrime_of_isPrime_prod_top'
 
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 theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Ideal S)).IsPrime :=
   by
   constructor
@@ -213,12 +144,6 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
   · exact Or.inr ⟨h, trivial⟩
 #align ideal.is_prime_ideal_prod_top Ideal.isPrime_ideal_prod_top
 
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 theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ideal R) I).IsPrime :=
   by
   rw [← map_prod_comm_prod]
@@ -226,12 +151,6 @@ theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ide
   exact is_prime_ideal_prod_top
 #align ideal.is_prime_ideal_prod_top' Ideal.isPrime_ideal_prod_top'
 
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-Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_auxₓ'. -/
 theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
     (Ideal.prod I J).IsPrime → I = ⊤ ∨ J = ⊤ :=
   by
@@ -240,12 +159,6 @@ theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
   exact fun ⟨hI, hJ⟩ hIJ => ⟨⟨0, 1⟩, ⟨1, 0⟩, by simp, by simp [hJ], by simp [hI]⟩
 #align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_aux
 
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-Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_prime Ideal.ideal_prod_primeₓ'. -/
 /-- Classification of prime ideals in product rings: the prime ideals of `R × S` are precisely the
     ideals of the form `p × S` or `R × p`, where `p` is a prime ideal of `R` or `S`. -/
 theorem ideal_prod_prime (I : Ideal (R × S)) :

93287238

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -96,10 +96,7 @@ theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I
   by
   ext
   rw [mem_map_iff_of_surjective (RingHom.fst R S) Prod.fst_surjective]
-  exact
-    ⟨by
-      rintro ⟨x, ⟨h, rfl⟩⟩
-      exact h.1, fun h => ⟨⟨x, 0⟩, ⟨⟨h, Ideal.zero_mem _⟩, rfl⟩⟩⟩
+  exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.1, fun h => ⟨⟨x, 0⟩, ⟨⟨h, Ideal.zero_mem _⟩, rfl⟩⟩⟩
 #align ideal.map_fst_prod Ideal.map_fst_prod
 
 /- warning: ideal.map_snd_prod -> Ideal.map_snd_prod is a dubious translation:
@@ -113,10 +110,7 @@ theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I
   by
   ext
   rw [mem_map_iff_of_surjective (RingHom.snd R S) Prod.snd_surjective]
-  exact
-    ⟨by
-      rintro ⟨x, ⟨h, rfl⟩⟩
-      exact h.2, fun h => ⟨⟨0, x⟩, ⟨⟨Ideal.zero_mem _, h⟩, rfl⟩⟩⟩
+  exact ⟨by rintro ⟨x, ⟨h, rfl⟩⟩; exact h.2, fun h => ⟨⟨0, x⟩, ⟨⟨Ideal.zero_mem _, h⟩, rfl⟩⟩⟩
 #align ideal.map_snd_prod Ideal.map_snd_prod
 
 /- warning: ideal.map_prod_comm_prod -> Ideal.map_prodComm_prod is a dubious translation:
@@ -210,8 +204,7 @@ Case conversion may be inaccurate. Consider using '#align ideal.is_prime_ideal_p
 theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Ideal S)).IsPrime :=
   by
   constructor
-  · rcases h with ⟨h, -⟩
-    contrapose! h
+  · rcases h with ⟨h, -⟩; contrapose! h
     rw [← prod_top_top, Prod.ext_iff] at h
     exact h.1
   rintro ⟨r₁, s₁⟩ ⟨r₂, s₂⟩ ⟨h₁, h₂⟩

93287238

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -120,10 +120,7 @@ theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I
 #align ideal.map_snd_prod Ideal.map_snd_prod
 
 /- warning: ideal.map_prod_comm_prod -> Ideal.map_prodComm_prod is a dubious translation:
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) (Prod.instMulProd.{u2, u1} S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Prod.instAddSum.{u1, u2} R S (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Distrib.toAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) (Prod.instAddSum.{u2, u1} S R (Distrib.toAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))) (RingEquiv.prodComm.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) (Ideal.prod.{u2, u1} S R _inst_2 _inst_1 J I)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.map_prod_comm_prod Ideal.map_prodComm_prodₓ'. -/
 @[simp]
 theorem map_prodComm_prod :

93287238

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -153,7 +153,7 @@ def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Eq.{succ (max u1 u2)} (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (coeFn.{max 1 (max (max (succ u1) (succ u2)) (succ (max u1 u2))) (succ (max u1 u2)) (succ u1) (succ u2), max (max (succ u1) (succ u2)) (succ (max u1 u2))} (Equiv.{max (succ u1) (succ u2), succ (max u1 u2)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (fun (_x : Equiv.{max (succ u1) (succ u2), succ (max u1 u2)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) => (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) -> (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Equiv.hasCoeToFun.{max (succ u1) (succ u2), succ (max u1 u2)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Equiv.symm.{succ (max u1 u2), max (succ u1) (succ u2)} (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.idealProdEquiv.{u1, u2} R S _inst_1 _inst_2)) (Prod.mk.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) I J)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Prod.mk.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) I J)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (fun (_x : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Equiv.symm.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.idealProdEquiv.{u1, u2} R S _inst_1 _inst_2)) (Prod.mk.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) I J)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Prod.mk.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) I J)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (fun (_x : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))) (Equiv.symm.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2))) (Prod.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.idealProdEquiv.{u1, u2} R S _inst_1 _inst_2)) (Prod.mk.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) I J)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)
 Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_equiv_symm_apply Ideal.idealProdEquiv_symm_applyₓ'. -/
 @[simp]
 theorem idealProdEquiv_symm_apply (I : Ideal R) (J : Ideal S) :

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: Markus Himmel
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.prod
-! leanprover-community/mathlib commit 052f6013363326d50cb99c6939814a4b8eb7b301
+! 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.RingTheory.Ideal.Operations
 /-!
 # Ideals in product rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 For commutative rings `R` and `S` and ideals `I ≤ R`, `J ≤ S`, we define `ideal.prod I J` as the
 product `I × J`, viewed as an ideal of `R × S`. In `ideal_prod_eq` we show that every ideal of
 `R × S` is of this form.  Furthermore, we show that every prime ideal of `R × S` is of the form

052f6013

bump to nightly-2023-03-18-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

73d15350

Diff

@@ -44,16 +44,12 @@ def prod : Ideal (R × S) where
     exact ⟨I.mul_mem_left _ hb₁, J.mul_mem_left _ hb₂⟩
 #align ideal.prod Ideal.prod
 
-/- warning: ideal.mem_prod -> Ideal.mem_prod is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_prod Ideal.mem_prodₓ'. -/
+#print Ideal.mem_prod /-
 @[simp]
 theorem mem_prod {r : R} {s : S} : (⟨r, s⟩ : R × S) ∈ prod I J ↔ r ∈ I ∧ s ∈ J :=
   Iff.rfl
 #align ideal.mem_prod Ideal.mem_prod
+-/
 
 /- warning: ideal.prod_top_top -> Ideal.prod_top_top is a dubious translation:
 lean 3 declaration is

052f6013

bump to nightly-2023-03-15-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

8a291292

Diff

@@ -26,6 +26,12 @@ variable {R : Type u} {S : Type v} [Ring R] [Ring S] (I I' : Ideal R) (J J' : Id
 
 namespace Ideal
 
+/- warning: ideal.prod -> Ideal.prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S], (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) -> (Ideal.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S], (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) -> (Ideal.{max u2 u1} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)))
+Case conversion may be inaccurate. Consider using '#align ideal.prod Ideal.prodₓ'. -/
 /-- `I × J` as an ideal of `R × S`. -/
 def prod : Ideal (R × S) where
   carrier := { x | x.fst ∈ I ∧ x.snd ∈ J }
@@ -38,16 +44,34 @@ def prod : Ideal (R × S) where
     exact ⟨I.mul_mem_left _ hb₁, J.mul_mem_left _ hb₂⟩
 #align ideal.prod Ideal.prod
 
+/- warning: ideal.mem_prod -> Ideal.mem_prod is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ideal.mem_prod Ideal.mem_prodₓ'. -/
 @[simp]
 theorem mem_prod {r : R} {s : S} : (⟨r, s⟩ : R × S) ∈ prod I J ↔ r ∈ I ∧ s ∈ J :=
   Iff.rfl
 #align ideal.mem_prod Ideal.mem_prod
 
+/- warning: ideal.prod_top_top -> Ideal.prod_top_top is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ideal.prod_top_top Ideal.prod_top_topₓ'. -/
 @[simp]
 theorem prod_top_top : prod (⊤ : Ideal R) (⊤ : Ideal S) = ⊤ :=
   Ideal.ext <| by simp
 #align ideal.prod_top_top Ideal.prod_top_top
 
+/- warning: ideal.ideal_prod_eq -> Ideal.ideal_prod_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_eq Ideal.ideal_prod_eqₓ'. -/
 /-- Every ideal of the product ring is of the form `I × J`, where `I` and `J` can be explicitly
     given as the image under the projection maps. -/
 theorem ideal_prod_eq (I : Ideal (R × S)) :
@@ -62,6 +86,12 @@ theorem ideal_prod_eq (I : Ideal (R × S)) :
   simpa using I.add_mem (I.mul_mem_left (1, 0) h₁) (I.mul_mem_left (0, 1) h₂)
 #align ideal.ideal_prod_eq Ideal.ideal_prod_eq
 
+/- warning: ideal.map_fst_prod -> Ideal.map_fst_prod is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.map.{max u2 u1, u1, max u1 u2} (Prod.{u1, u2} R S) R (RingHom.{max u2 u1, u1} (Prod.{u1, u2} R S) R (Prod.instNonAssocSemiringProd.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ring.toSemiring.{u1} R _inst_1) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (Prod.{u1, u2} R S) R (Prod.instNonAssocSemiringProd.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.fst.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) I
+Case conversion may be inaccurate. Consider using '#align ideal.map_fst_prod Ideal.map_fst_prodₓ'. -/
 @[simp]
 theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I J) = I :=
   by
@@ -73,6 +103,12 @@ theorem map_fst_prod (I : Ideal R) (J : Ideal S) : map (RingHom.fst R S) (prod I
       exact h.1, fun h => ⟨⟨x, 0⟩, ⟨⟨h, Ideal.zero_mem _⟩, rfl⟩⟩⟩
 #align ideal.map_fst_prod Ideal.map_fst_prod
 
+/- warning: ideal.map_snd_prod -> Ideal.map_snd_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)), Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{max u1 u2, u2, max u1 u2} (Prod.{u1, u2} R S) S (RingHom.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{max u1 u2, u2} (Prod.{u1, u2} R S) S (Prod.nonAssocSemiring.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (RingHom.snd.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) J
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ideal.map_snd_prod Ideal.map_snd_prodₓ'. -/
 @[simp]
 theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I J) = J :=
   by
@@ -84,6 +120,12 @@ theorem map_snd_prod (I : Ideal R) (J : Ideal S) : map (RingHom.snd R S) (prod I
       exact h.2, fun h => ⟨⟨0, x⟩, ⟨⟨Ideal.zero_mem _, h⟩, rfl⟩⟩⟩
 #align ideal.map_snd_prod Ideal.map_snd_prod
 
+/- warning: ideal.map_prod_comm_prod -> Ideal.map_prodComm_prod is a dubious translation:
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S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))))) (Prod.hasAdd.{u1, u2} R S (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))))) (Prod.hasMul.{u2, u1} S R (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (Prod.hasAdd.{u2, u1} S R (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))))) (RingEquiv.prodComm.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) (Ideal.prod.{u2, u1} S R _inst_2 _inst_1 J I)
+but is expected to have type
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 @[simp]
 theorem map_prodComm_prod :
     map ((RingEquiv.prodComm : R × S ≃+* S × R) : R × S →+* S × R) (prod I J) = prod J I :=
@@ -92,6 +134,12 @@ theorem map_prodComm_prod :
   simp [map_map]
 #align ideal.map_prod_comm_prod Ideal.map_prodComm_prod
 
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 /-- Ideals of `R × S` are in one-to-one correspondence with pairs of ideals of `R` and ideals of
     `S`. -/
 def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
@@ -102,17 +150,35 @@ def idealProdEquiv : Ideal (R × S) ≃ Ideal R × Ideal S
   right_inv := fun ⟨I, J⟩ => by simp
 #align ideal.ideal_prod_equiv Ideal.idealProdEquiv
 
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 @[simp]
 theorem idealProdEquiv_symm_apply (I : Ideal R) (J : Ideal S) :
     idealProdEquiv.symm ⟨I, J⟩ = prod I J :=
   rfl
 #align ideal.ideal_prod_equiv_symm_apply Ideal.idealProdEquiv_symm_apply
 
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 theorem prod.ext_iff {I I' : Ideal R} {J J' : Ideal S} : prod I J = prod I' J' ↔ I = I' ∧ J = J' :=
   by
   simp only [← ideal_prod_equiv_symm_apply, ideal_prod_equiv.symm.injective.eq_iff, Prod.mk.inj_iff]
 #align ideal.prod.ext_iff Ideal.prod.ext_iff
 
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+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.instTopSubmodule.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R _inst_1) I)
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_of_is_prime_prod_top Ideal.isPrime_of_isPrime_prod_topₓ'. -/
 theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Ideal S)).IsPrime) :
     I.IsPrime := by
   constructor
@@ -126,6 +192,12 @@ theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Idea
     simpa using h.mem_or_mem this
 #align ideal.is_prime_of_is_prime_prod_top Ideal.isPrime_of_isPrime_prod_top
 
+/- warning: ideal.is_prime_of_is_prime_prod_top' -> Ideal.isPrime_of_isPrime_prod_top' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, (Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) I)) -> (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S _inst_2) I)
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, (Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) I)) -> (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S _inst_2) I)
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_of_is_prime_prod_top' Ideal.isPrime_of_isPrime_prod_top'ₓ'. -/
 theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal R) I).IsPrime) :
     I.IsPrime := by
   apply @is_prime_of_is_prime_prod_top _ R
@@ -133,6 +205,12 @@ theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal
   exact map_is_prime_of_equiv _
 #align ideal.is_prime_of_is_prime_prod_top' Ideal.isPrime_of_isPrime_prod_top'
 
+/- warning: ideal.is_prime_ideal_prod_top -> Ideal.isPrime_ideal_prod_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} [h : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R _inst_1) I], Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.hasTop.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} [h : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R _inst_1) I], Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.instTopSubmodule.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_ideal_prod_top Ideal.isPrime_ideal_prod_topₓ'. -/
 theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Ideal S)).IsPrime :=
   by
   constructor
@@ -146,6 +224,12 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
   · exact Or.inr ⟨h, trivial⟩
 #align ideal.is_prime_ideal_prod_top Ideal.isPrime_ideal_prod_top
 
+/- warning: ideal.is_prime_ideal_prod_top' -> Ideal.isPrime_ideal_prod_top' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)} [h : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S _inst_2) I], Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) I)
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)} [h : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S _inst_2) I], Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) I)
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_ideal_prod_top' Ideal.isPrime_ideal_prod_top'ₓ'. -/
 theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ideal R) I).IsPrime :=
   by
   rw [← map_prod_comm_prod]
@@ -153,6 +237,12 @@ theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ide
   exact is_prime_ideal_prod_top
 #align ideal.is_prime_ideal_prod_top' Ideal.isPrime_ideal_prod_top'
 
+/- warning: ideal.ideal_prod_prime_aux -> Ideal.ideal_prod_prime_aux is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, (Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.semiring.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) -> (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) J (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.hasTop.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, (Ideal.IsPrime.{max u1 u2} (Prod.{u1, u2} R S) (Prod.instSemiringProd.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)) (Ideal.prod.{u1, u2} R S _inst_1 _inst_2 I J)) -> (Or (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) J (Top.top.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.instTopSubmodule.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_auxₓ'. -/
 theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
     (Ideal.prod I J).IsPrime → I = ⊤ ∨ J = ⊤ :=
   by
@@ -161,6 +251,12 @@ theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :
   exact fun ⟨hI, hJ⟩ hIJ => ⟨⟨0, 1⟩, ⟨1, 0⟩, by simp, by simp [hJ], by simp [hI]⟩
 #align ideal.ideal_prod_prime_aux Ideal.ideal_prod_prime_aux
 
+/- warning: ideal.ideal_prod_prime -> Ideal.ideal_prod_prime is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ideal.ideal_prod_prime Ideal.ideal_prod_primeₓ'. -/
 /-- Classification of prime ideals in product rings: the prime ideals of `R × S` are precisely the
     ideals of the form `p × S` or `R × p`, where `p` is a prime ideal of `R` or `S`. -/
 theorem ideal_prod_prime (I : Ideal (R × S)) :

052f6013

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

052f6013

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -121,9 +121,10 @@ theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Idea
 
 theorem isPrime_of_isPrime_prod_top' {I : Ideal S} (h : (Ideal.prod (⊤ : Ideal R) I).IsPrime) :
     I.IsPrime := by
-  apply @isPrime_of_isPrime_prod_top _ R
+  apply isPrime_of_isPrime_prod_top (S := R)
   rw [← map_prodComm_prod]
-  exact map_isPrime_of_equiv _
+  -- Note: couldn't synthesize the right instances without the `R` and `S` hints
+  exact map_isPrime_of_equiv (RingEquiv.prodComm (R := R) (S := S))
 #align ideal.is_prime_of_is_prime_prod_top' Ideal.isPrime_of_isPrime_prod_top'
 
 theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Ideal S)).IsPrime := by
@@ -141,7 +142,8 @@ theorem isPrime_ideal_prod_top {I : Ideal R} [h : I.IsPrime] : (prod I (⊤ : Id
 theorem isPrime_ideal_prod_top' {I : Ideal S} [h : I.IsPrime] : (prod (⊤ : Ideal R) I).IsPrime := by
   letI : IsPrime (prod I (⊤ : Ideal R)) := isPrime_ideal_prod_top
   rw [← map_prodComm_prod]
-  apply map_isPrime_of_equiv _
+  -- Note: couldn't synthesize the right instances without the `R` and `S` hints
+  exact map_isPrime_of_equiv (RingEquiv.prodComm (R := S) (S := R))
 #align ideal.is_prime_ideal_prod_top' Ideal.isPrime_ideal_prod_top'
 
 theorem ideal_prod_prime_aux {I : Ideal R} {J : Ideal S} :

052f6013

feat (Mathlib.RingTheory.Ideal.Operations) : Change hypotheses from ring to semiring (#8469)

Moved some results from ring to semiring.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com>

49383962

Diff

@@ -19,7 +19,7 @@ product `I × J`, viewed as an ideal of `R × S`. In `ideal_prod_eq` we show tha
 
 universe u v
 
-variable {R : Type u} {S : Type v} [Ring R] [Ring S] (I I' : Ideal R) (J J' : Ideal S)
+variable {R : Type u} {S : Type v} [Semiring R] [Semiring S] (I I' : Ideal R) (J J' : Ideal S)
 
 namespace Ideal

052f6013

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) 2020 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module ring_theory.ideal.prod
-! leanprover-community/mathlib commit 052f6013363326d50cb99c6939814a4b8eb7b301
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Ideal.Operations
 
+#align_import ring_theory.ideal.prod from "leanprover-community/mathlib"@"052f6013363326d50cb99c6939814a4b8eb7b301"
+
 /-!
 # Ideals in product rings

052f6013

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

@@ -165,10 +165,10 @@ theorem ideal_prod_prime (I : Ideal (R × S)) :
     intro hI
     rcases ideal_prod_prime_aux hI with (h | h)
     · right
-      rw [h] at hI⊢
+      rw [h] at hI ⊢
       exact ⟨_, ⟨isPrime_of_isPrime_prod_top' hI, rfl⟩⟩
     · left
-      rw [h] at hI⊢
+      rw [h] at hI ⊢
       exact ⟨_, ⟨isPrime_of_isPrime_prod_top hI, rfl⟩⟩
   · rintro (⟨p, ⟨h, rfl⟩⟩ | ⟨p, ⟨h, rfl⟩⟩)
     · exact isPrime_ideal_prod_top

052f6013

chore: cleanup various notes about etaExperiment (#4029)

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

ecb752ad

Diff

@@ -48,10 +48,6 @@ theorem prod_top_top : prod (⊤ : Ideal R) (⊤ : Ideal S) = ⊤ :=
   Ideal.ext <| by simp
 #align ideal.prod_top_top Ideal.prod_top_top
 
-/- Porting note: This is necessary to prevent failing type class searches in
-`map (RingHom.fst R S) I`, remove when `etaExperiment` becomes the default. -/
-attribute [-instance] Ring.toNonAssocRing
-
 /-- Every ideal of the product ring is of the form `I × J`, where `I` and `J` can be explicitly
     given as the image under the projection maps. -/
 theorem ideal_prod_eq (I : Ideal (R × S)) :

052f6013

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -108,8 +108,8 @@ theorem idealProdEquiv_symm_apply (I : Ideal R) (J : Ideal S) :
   rfl
 #align ideal.ideal_prod_equiv_symm_apply Ideal.idealProdEquiv_symm_apply
 
-theorem prod.ext_iff {I I' : Ideal R} {J J' : Ideal S} : prod I J = prod I' J' ↔ I = I' ∧ J = J' :=
-  by
+theorem prod.ext_iff {I I' : Ideal R} {J J' : Ideal S} :
+    prod I J = prod I' J' ↔ I = I' ∧ J = J' := by
   simp only [← idealProdEquiv_symm_apply, idealProdEquiv.symm.injective.eq_iff, Prod.mk.inj_iff]
 #align ideal.prod.ext_iff Ideal.prod.ext_iff
 
@@ -120,8 +120,7 @@ theorem isPrime_of_isPrime_prod_top {I : Ideal R} (h : (Ideal.prod I (⊤ : Idea
     rw [h, prod_top_top, isPrime_iff]
     simp [isPrime_iff, h]
   · intro x y hxy
-    have : (⟨x, 1⟩ : R × S) * ⟨y, 1⟩ ∈ prod I ⊤ :=
-      by
+    have : (⟨x, 1⟩ : R × S) * ⟨y, 1⟩ ∈ prod I ⊤ := by
       rw [Prod.mk_mul_mk, mul_one, mem_prod]
       exact ⟨hxy, trivial⟩
     simpa using h.mem_or_mem this

052f6013

feat: port RingTheory.Ideal.Prod (#2877)

a85bc07a

`ring_theory.ideal.prod` ⟷ `Mathlib.RingTheory.Ideal.Prod`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 451

ring_theory.ideal.prod ⟷ Mathlib.RingTheory.Ideal.Prod

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 451

`ring_theory.ideal.prod` ⟷ `Mathlib.RingTheory.Ideal.Prod`

`simp` not firing sometimes