ring_theory.ideal.associated_prime | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

f0c8bf92

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

b5ad1414

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -95,7 +95,7 @@ theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedP
   rintro ⟨hI, x, hx⟩
   apply hI.ne_top
   rwa [Subsingleton.elim x 0, submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at
-    hx 
+    hx
 #align not_is_associated_prime_of_subsingleton not_isAssociatedPrime_of_subsingleton
 -/
 
@@ -115,7 +115,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
   intro a b hab
   rw [Classical.or_iff_not_imp_left]
   intro ha
-  rw [Submodule.mem_annihilator_span_singleton] at ha hab 
+  rw [Submodule.mem_annihilator_span_singleton] at ha hab
   have H₁ : (R ∙ y).annihilator ≤ (R ∙ a • y).annihilator :=
     by
     intro c hc
@@ -180,7 +180,7 @@ theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J
   obtain ⟨hJ, x, e⟩ := h
   have : x ≠ 0 := by
     rintro rfl; apply hJ.1
-    rwa [submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e 
+    rwa [submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e
   obtain ⟨x, rfl⟩ := Ideal.Quotient.mkₐ_surjective R _ x
   replace e : ∀ {y}, y ∈ J ↔ x * y ∈ I
   · intro y;

b5ad1414

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -113,7 +113,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
       ⟨(R ∙ x).annihilator, rfl.le, this, x, rfl⟩
   refine' ⟨_, ⟨⟨h₁, _⟩, y, rfl⟩, l⟩
   intro a b hab
-  rw [or_iff_not_imp_left]
+  rw [Classical.or_iff_not_imp_left]
   intro ha
   rw [Submodule.mem_annihilator_span_singleton] at ha hab 
   have H₁ : (R ∙ y).annihilator ≤ (R ∙ a • y).annihilator :=

b5ad1414

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.LinearAlgebra.Span
-import Mathbin.RingTheory.Ideal.Operations
-import Mathbin.RingTheory.Ideal.QuotientOperations
-import Mathbin.RingTheory.Noetherian
+import LinearAlgebra.Span
+import RingTheory.Ideal.Operations
+import RingTheory.Ideal.QuotientOperations
+import RingTheory.Noetherian
 
 #align_import ring_theory.ideal.associated_prime from "leanprover-community/mathlib"@"b5ad141426bb005414324f89719c77c0aa3ec612"

b5ad1414

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.ideal.associated_prime
-! leanprover-community/mathlib commit b5ad141426bb005414324f89719c77c0aa3ec612
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Span
 import Mathbin.RingTheory.Ideal.Operations
 import Mathbin.RingTheory.Ideal.QuotientOperations
 import Mathbin.RingTheory.Noetherian
 
+#align_import ring_theory.ideal.associated_prime from "leanprover-community/mathlib"@"b5ad141426bb005414324f89719c77c0aa3ec612"
+
 /-!
 
 # Associated primes of a module

b5ad1414

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -62,14 +62,19 @@ variable {I J M R} (h : IsAssociatedPrime I M)
 
 variable {M' : Type _} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 
+#print AssociatePrimes.mem_iff /-
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M :=
   Iff.rfl
 #align associate_primes.mem_iff AssociatePrimes.mem_iff
+-/
 
+#print IsAssociatedPrime.isPrime /-
 theorem IsAssociatedPrime.isPrime : I.IsPrime :=
   h.1
 #align is_associated_prime.is_prime IsAssociatedPrime.isPrime
+-/
 
+#print IsAssociatedPrime.map_of_injective /-
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
   obtain ⟨x, rfl⟩ := h.2
@@ -78,11 +83,14 @@ theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Fun
   rw [Submodule.mem_annihilator_span_singleton, Submodule.mem_annihilator_span_singleton, ←
     map_smul, ← f.map_zero, hf.eq_iff]
 #align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injective
+-/
 
+#print LinearEquiv.isAssociatedPrime_iff /-
 theorem LinearEquiv.isAssociatedPrime_iff (l : M ≃ₗ[R] M') :
     IsAssociatedPrime I M ↔ IsAssociatedPrime I M' :=
   ⟨fun h => h.map_of_injective l l.Injective, fun h => h.map_of_injective l.symm l.symm.Injective⟩
 #align linear_equiv.is_associated_prime_iff LinearEquiv.isAssociatedPrime_iff
+-/
 
 #print not_isAssociatedPrime_of_subsingleton /-
 theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedPrime I M :=
@@ -96,6 +104,7 @@ theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedP
 
 variable (R)
 
+#print exists_le_isAssociatedPrime_of_isNoetherianRing /-
 theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R] (x : M)
     (hx : x ≠ 0) : ∃ P : Ideal R, IsAssociatedPrime P M ∧ (R ∙ x).annihilator ≤ P :=
   by
@@ -120,18 +129,23 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
   rwa [H₁.eq_of_not_lt (h₃ (R ∙ a • y).annihilator ⟨l.trans H₁, H₂, _, rfl⟩),
     Submodule.mem_annihilator_span_singleton, smul_comm, smul_smul]
 #align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRing
+-/
 
 variable {R}
 
+#print associatedPrimes.subset_of_injective /-
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf
 #align associated_primes.subset_of_injective associatedPrimes.subset_of_injective
+-/
 
+#print LinearEquiv.AssociatedPrimes.eq /-
 theorem LinearEquiv.AssociatedPrimes.eq (l : M ≃ₗ[R] M') :
     associatedPrimes R M = associatedPrimes R M' :=
   le_antisymm (associatedPrimes.subset_of_injective l l.Injective)
     (associatedPrimes.subset_of_injective l.symm l.symm.Injective)
 #align linear_equiv.associated_primes.eq LinearEquiv.AssociatedPrimes.eq
+-/
 
 #print associatedPrimes.eq_empty_of_subsingleton /-
 theorem associatedPrimes.eq_empty_of_subsingleton [Subsingleton M] : associatedPrimes R M = ∅ := by
@@ -142,6 +156,7 @@ theorem associatedPrimes.eq_empty_of_subsingleton [Subsingleton M] : associatedP
 
 variable (R M)
 
+#print associatedPrimes.nonempty /-
 theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
     (associatedPrimes R M).Nonempty :=
   by
@@ -149,15 +164,18 @@ theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
   obtain ⟨P, hP, _⟩ := exists_le_isAssociatedPrime_of_isNoetherianRing R x hx
   exact ⟨P, hP⟩
 #align associated_primes.nonempty associatedPrimes.nonempty
+-/
 
 variable {R M}
 
+#print IsAssociatedPrime.annihilator_le /-
 theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
     (⊤ : Submodule R M).annihilator ≤ I :=
   by
   obtain ⟨hI, x, rfl⟩ := h
   exact Submodule.annihilator_mono le_top
 #align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_le
+-/
 
 #print IsAssociatedPrime.eq_radical /-
 theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J (R ⧸ I)) :

b5ad1414

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -54,7 +54,7 @@ variable (R)
 #print associatedPrimes /-
 /-- The set of associated primes of a module. -/
 def associatedPrimes : Set (Ideal R) :=
-  { I | IsAssociatedPrime I M }
+  {I | IsAssociatedPrime I M}
 #align associated_primes associatedPrimes
 -/
 
@@ -103,7 +103,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
     rwa [Ne.def, Ideal.eq_top_iff_one, Submodule.mem_annihilator_span_singleton, one_smul]
   obtain ⟨P, ⟨l, h₁, y, rfl⟩, h₃⟩ :=
     set_has_maximal_iff_noetherian.mpr H
-      { P | (R ∙ x).annihilator ≤ P ∧ P ≠ ⊤ ∧ ∃ y : M, P = (R ∙ y).annihilator }
+      {P | (R ∙ x).annihilator ≤ P ∧ P ≠ ⊤ ∧ ∃ y : M, P = (R ∙ y).annihilator}
       ⟨(R ∙ x).annihilator, rfl.le, this, x, rfl⟩
   refine' ⟨_, ⟨⟨h₁, _⟩, y, rfl⟩, l⟩
   intro a b hab

b5ad1414

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -90,7 +90,7 @@ theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedP
   rintro ⟨hI, x, hx⟩
   apply hI.ne_top
   rwa [Subsingleton.elim x 0, submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at
-    hx
+    hx 
 #align not_is_associated_prime_of_subsingleton not_isAssociatedPrime_of_subsingleton
 -/
 
@@ -109,11 +109,11 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
   intro a b hab
   rw [or_iff_not_imp_left]
   intro ha
-  rw [Submodule.mem_annihilator_span_singleton] at ha hab
+  rw [Submodule.mem_annihilator_span_singleton] at ha hab 
   have H₁ : (R ∙ y).annihilator ≤ (R ∙ a • y).annihilator :=
     by
     intro c hc
-    rw [Submodule.mem_annihilator_span_singleton] at hc⊢
+    rw [Submodule.mem_annihilator_span_singleton] at hc ⊢
     rw [smul_comm, hc, smul_zero]
   have H₂ : (Submodule.span R {a • y}).annihilator ≠ ⊤ := by
     rwa [Ne.def, Submodule.annihilator_eq_top_iff, Submodule.span_singleton_eq_bot]
@@ -165,7 +165,7 @@ theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J
   obtain ⟨hJ, x, e⟩ := h
   have : x ≠ 0 := by
     rintro rfl; apply hJ.1
-    rwa [submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e
+    rwa [submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e 
   obtain ⟨x, rfl⟩ := Ideal.Quotient.mkₐ_surjective R _ x
   replace e : ∀ {y}, y ∈ J ↔ x * y ∈ I
   · intro y;

b5ad1414

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -62,32 +62,14 @@ variable {I J M R} (h : IsAssociatedPrime I M)
 
 variable {M' : Type _} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 
-/- warning: associate_primes.mem_iff -> AssociatePrimes.mem_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], Iff (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) I (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (Membership.mem.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Set.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Set.instMembershipSet.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) I (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3)
-Case conversion may be inaccurate. Consider using '#align associate_primes.mem_iff AssociatePrimes.mem_iffₓ'. -/
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M :=
   Iff.rfl
 #align associate_primes.mem_iff AssociatePrimes.mem_iff
 
-/- warning: is_associated_prime.is_prime -> IsAssociatedPrime.isPrime is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) I)
-Case conversion may be inaccurate. Consider using '#align is_associated_prime.is_prime IsAssociatedPrime.isPrimeₓ'. -/
 theorem IsAssociatedPrime.isPrime : I.IsPrime :=
   h.1
 #align is_associated_prime.is_prime IsAssociatedPrime.isPrime
 
-/- warning: is_associated_prime.map_of_injective -> IsAssociatedPrime.map_of_injective is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injectiveₓ'. -/
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
   obtain ⟨x, rfl⟩ := h.2
@@ -97,12 +79,6 @@ theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Fun
     map_smul, ← f.map_zero, hf.eq_iff]
 #align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injective
 
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-Case conversion may be inaccurate. Consider using '#align linear_equiv.is_associated_prime_iff LinearEquiv.isAssociatedPrime_iffₓ'. -/
 theorem LinearEquiv.isAssociatedPrime_iff (l : M ≃ₗ[R] M') :
     IsAssociatedPrime I M ↔ IsAssociatedPrime I M' :=
   ⟨fun h => h.map_of_injective l l.Injective, fun h => h.map_of_injective l.symm l.symm.Injective⟩
@@ -120,12 +96,6 @@ theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedP
 
 variable (R)
 
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-Case conversion may be inaccurate. Consider using '#align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRingₓ'. -/
 theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R] (x : M)
     (hx : x ≠ 0) : ∃ P : Ideal R, IsAssociatedPrime P M ∧ (R ∙ x).annihilator ≤ P :=
   by
@@ -153,22 +123,10 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
 
 variable {R}
 
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-Case conversion may be inaccurate. Consider using '#align associated_primes.subset_of_injective associatedPrimes.subset_of_injectiveₓ'. -/
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf
 #align associated_primes.subset_of_injective associatedPrimes.subset_of_injective
 
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-Case conversion may be inaccurate. Consider using '#align linear_equiv.associated_primes.eq LinearEquiv.AssociatedPrimes.eqₓ'. -/
 theorem LinearEquiv.AssociatedPrimes.eq (l : M ≃ₗ[R] M') :
     associatedPrimes R M = associatedPrimes R M' :=
   le_antisymm (associatedPrimes.subset_of_injective l l.Injective)
@@ -184,12 +142,6 @@ theorem associatedPrimes.eq_empty_of_subsingleton [Subsingleton M] : associatedP
 
 variable (R M)
 
-/- warning: associated_primes.nonempty -> associatedPrimes.nonempty is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_7 : Nontrivial.{u2} M], Set.Nonempty.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align associated_primes.nonempty associatedPrimes.nonemptyₓ'. -/
 theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
     (associatedPrimes R M).Nonempty :=
   by
@@ -200,12 +152,6 @@ theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
 
 variable {R M}
 
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-Case conversion may be inaccurate. Consider using '#align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_leₓ'. -/
 theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
     (⊤ : Submodule R M).annihilator ≤ I :=
   by

b5ad1414

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -218,20 +218,17 @@ theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J
     J = I.radical := by
   obtain ⟨hJ, x, e⟩ := h
   have : x ≠ 0 := by
-    rintro rfl
-    apply hJ.1
+    rintro rfl; apply hJ.1
     rwa [submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e
   obtain ⟨x, rfl⟩ := Ideal.Quotient.mkₐ_surjective R _ x
   replace e : ∀ {y}, y ∈ J ↔ x * y ∈ I
-  · intro y
+  · intro y;
     rw [e, Submodule.mem_annihilator_span_singleton, ← map_smul, smul_eq_mul, mul_comm,
       Ideal.Quotient.mkₐ_eq_mk, ← Ideal.Quotient.mk_eq_mk, Submodule.Quotient.mk_eq_zero]
   apply le_antisymm
   · intro y hy
     exact (hI.2 <| e.mp hy).resolve_left ((Submodule.Quotient.mk_eq_zero I).Not.mp this)
-  · rw [hJ.radical_le_iff]
-    intro y hy
-    exact e.mpr (I.mul_mem_left x hy)
+  · rw [hJ.radical_le_iff]; intro y hy; exact e.mpr (I.mul_mem_left x hy)
 #align is_associated_prime.eq_radical IsAssociatedPrime.eq_radical
 -/

b5ad1414

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -86,7 +86,7 @@ theorem IsAssociatedPrime.isPrime : I.IsPrime :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (IsAssociatedPrime.{u1, u3} R _inst_1 I M' _inst_4 _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injectiveₓ'. -/
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
@@ -157,7 +157,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSubset.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u3} R _inst_1 M' _inst_4 _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
 Case conversion may be inaccurate. Consider using '#align associated_primes.subset_of_injective associatedPrimes.subset_of_injectiveₓ'. -/
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf

b5ad1414

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -86,7 +86,7 @@ theorem IsAssociatedPrime.isPrime : I.IsPrime :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (IsAssociatedPrime.{u1, u3} R _inst_1 I M' _inst_4 _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injectiveₓ'. -/
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
@@ -157,7 +157,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSubset.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u3} R _inst_1 M' _inst_4 _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
 Case conversion may be inaccurate. Consider using '#align associated_primes.subset_of_injective associatedPrimes.subset_of_injectiveₓ'. -/
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf

b5ad1414

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -122,7 +122,7 @@ variable (R)
 
 /- warning: exists_le_is_associated_prime_of_is_noetherian_ring -> exists_le_isAssociatedPrime_of_isNoetherianRing is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (IsAssociatedPrime.{u1, u2} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) P)))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (IsAssociatedPrime.{u1, u2} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) P)))
 but is expected to have type
   forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [H : IsNoetherianRing.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] (x : M), (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))) -> (Exists.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (P : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => And (IsAssociatedPrime.{u2, u1} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) x))) P)))
 Case conversion may be inaccurate. Consider using '#align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRingₓ'. -/
@@ -202,7 +202,7 @@ variable {R M}
 
 /- warning: is_associated_prime.annihilator_le -> IsAssociatedPrime.annihilator_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) I)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) I)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) I)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_leₓ'. -/

b5ad1414

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -66,7 +66,7 @@ variable {M' : Type _} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], Iff (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) I (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (Membership.mem.{u2, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Set.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (Set.instMembershipSet.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) I (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (Membership.mem.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Set.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Set.instMembershipSet.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) I (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align associate_primes.mem_iff AssociatePrimes.mem_iffₓ'. -/
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M :=
   Iff.rfl
@@ -76,7 +76,7 @@ theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPri
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) I)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) I)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.is_prime IsAssociatedPrime.isPrimeₓ'. -/
 theorem IsAssociatedPrime.isPrime : I.IsPrime :=
   h.1
@@ -86,7 +86,7 @@ theorem IsAssociatedPrime.isPrime : I.IsPrime :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (IsAssociatedPrime.{u1, u3} R _inst_1 I M' _inst_4 _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injectiveₓ'. -/
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
@@ -101,7 +101,7 @@ theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Fun
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)], (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) -> (Iff (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) (IsAssociatedPrime.{u1, u3} R _inst_1 I M' _inst_4 _inst_5))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)], (LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) -> (Iff (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)], (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) -> (Iff (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.is_associated_prime_iff LinearEquiv.isAssociatedPrime_iffₓ'. -/
 theorem LinearEquiv.isAssociatedPrime_iff (l : M ≃ₗ[R] M') :
     IsAssociatedPrime I M ↔ IsAssociatedPrime I M' :=
@@ -124,7 +124,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (IsAssociatedPrime.{u1, u2} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) P)))
 but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] (x : M), (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))) -> (Exists.{succ u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (fun (P : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) => And (IsAssociatedPrime.{u2, u1} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) x))) P)))
+  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [H : IsNoetherianRing.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] (x : M), (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))) -> (Exists.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (P : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => And (IsAssociatedPrime.{u2, u1} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) x))) P)))
 Case conversion may be inaccurate. Consider using '#align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRingₓ'. -/
 theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R] (x : M)
     (hx : x ≠ 0) : ∃ P : Ideal R, IsAssociatedPrime P M ∧ (R ∙ x).annihilator ≤ P :=
@@ -157,7 +157,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSubset.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u3} R _inst_1 M' _inst_4 _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u3}} [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u1, u3} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] {M' : Type.{u2}} [_inst_4 : AddCommGroup.{u2} M'] [_inst_5 : Module.{u1, u2} R M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4)] (f : LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u3, succ u2} M M' (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u1, u1, u3, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u2} R R M M' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)) -> (HasSubset.Subset.{u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instHasSubsetSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (associatedPrimes.{u1, u3} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u2} R _inst_1 M' _inst_4 _inst_5))
 Case conversion may be inaccurate. Consider using '#align associated_primes.subset_of_injective associatedPrimes.subset_of_injectiveₓ'. -/
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf
@@ -167,7 +167,7 @@ theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)], (LinearEquiv.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) -> (Eq.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u1, u3} R _inst_1 M' _inst_4 _inst_5))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)], (LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) -> (Eq.{succ u3} (Set.{u3} (Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (associatedPrimes.{u3, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u3, u1} R _inst_1 M' _inst_4 _inst_5))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)], (LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) -> (Eq.{succ u3} (Set.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (associatedPrimes.{u3, u2} R _inst_1 M _inst_2 _inst_3) (associatedPrimes.{u3, u1} R _inst_1 M' _inst_4 _inst_5))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.associated_primes.eq LinearEquiv.AssociatedPrimes.eqₓ'. -/
 theorem LinearEquiv.AssociatedPrimes.eq (l : M ≃ₗ[R] M') :
     associatedPrimes R M = associatedPrimes R M' :=
@@ -188,7 +188,7 @@ variable (R M)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_7 : Nontrivial.{u2} M], Set.Nonempty.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)
 but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_6 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] [_inst_7 : Nontrivial.{u1} M], Set.Nonempty.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)
+  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_6 : IsNoetherianRing.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_7 : Nontrivial.{u1} M], Set.Nonempty.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align associated_primes.nonempty associatedPrimes.nonemptyₓ'. -/
 theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
     (associatedPrimes R M).Nonempty :=
@@ -204,7 +204,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) I)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) I)
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) I)
 Case conversion may be inaccurate. Consider using '#align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_leₓ'. -/
 theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
     (⊤ : Submodule R M).annihilator ≤ I :=

b5ad1414

bump to nightly-2023-05-08-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

508651e1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.associated_prime
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit b5ad141426bb005414324f89719c77c0aa3ec612
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.RingTheory.Noetherian
 
 # Associated primes of a module
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We provide the definition and related lemmas about associated primes of modules.
 
 ## Main definition

f0c8bf92

bump to nightly-2023-05-06-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

c6fb1d2b

Diff

@@ -39,30 +39,52 @@ Generalize this to a non-commutative setting once there are annihilator for non-
 
 variable {R : Type _} [CommRing R] (I J : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
 
+#print IsAssociatedPrime /-
 /-- `is_associated_prime I M` if the prime ideal `I` is the annihilator of some `x : M`. -/
 def IsAssociatedPrime : Prop :=
   I.IsPrime ∧ ∃ x : M, I = (R ∙ x).annihilator
 #align is_associated_prime IsAssociatedPrime
+-/
 
 variable (R)
 
+#print associatedPrimes /-
 /-- The set of associated primes of a module. -/
 def associatedPrimes : Set (Ideal R) :=
   { I | IsAssociatedPrime I M }
 #align associated_primes associatedPrimes
+-/
 
 variable {I J M R} (h : IsAssociatedPrime I M)
 
 variable {M' : Type _} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 
+/- warning: associate_primes.mem_iff -> AssociatePrimes.mem_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], Iff (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) I (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], Iff (Membership.mem.{u2, u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Set.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (Set.instMembershipSet.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) I (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)) (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align associate_primes.mem_iff AssociatePrimes.mem_iffₓ'. -/
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M :=
   Iff.rfl
 #align associate_primes.mem_iff AssociatePrimes.mem_iff
 
+/- warning: is_associated_prime.is_prime -> IsAssociatedPrime.isPrime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (Ideal.IsPrime.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) I)
+Case conversion may be inaccurate. Consider using '#align is_associated_prime.is_prime IsAssociatedPrime.isPrimeₓ'. -/
 theorem IsAssociatedPrime.isPrime : I.IsPrime :=
   h.1
 #align is_associated_prime.is_prime IsAssociatedPrime.isPrime
 
+/- warning: is_associated_prime.map_of_injective -> IsAssociatedPrime.map_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) -> (IsAssociatedPrime.{u1, u3} R _inst_1 I M' _inst_4 _inst_5)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)] (f : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5), (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) -> (Function.Injective.{succ u2, succ u1} M M' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u1} R R M M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1))))) f)) -> (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injectiveₓ'. -/
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
   obtain ⟨x, rfl⟩ := h.2
@@ -72,11 +94,18 @@ theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Fun
     map_smul, ← f.map_zero, hf.eq_iff]
 #align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injective
 
+/- warning: linear_equiv.is_associated_prime_iff -> LinearEquiv.isAssociatedPrime_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {I : Ideal.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u1}} [_inst_4 : AddCommGroup.{u1} M'] [_inst_5 : Module.{u3, u1} R M' (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4)], (LinearEquiv.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M' _inst_4) _inst_3 _inst_5) -> (Iff (IsAssociatedPrime.{u3, u2} R _inst_1 I M _inst_2 _inst_3) (IsAssociatedPrime.{u3, u1} R _inst_1 I M' _inst_4 _inst_5))
+Case conversion may be inaccurate. Consider using '#align linear_equiv.is_associated_prime_iff LinearEquiv.isAssociatedPrime_iffₓ'. -/
 theorem LinearEquiv.isAssociatedPrime_iff (l : M ≃ₗ[R] M') :
     IsAssociatedPrime I M ↔ IsAssociatedPrime I M' :=
   ⟨fun h => h.map_of_injective l l.Injective, fun h => h.map_of_injective l.symm l.symm.Injective⟩
 #align linear_equiv.is_associated_prime_iff LinearEquiv.isAssociatedPrime_iff
 
+#print not_isAssociatedPrime_of_subsingleton /-
 theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedPrime I M :=
   by
   rintro ⟨hI, x, hx⟩
@@ -84,9 +113,16 @@ theorem not_isAssociatedPrime_of_subsingleton [Subsingleton M] : ¬IsAssociatedP
   rwa [Subsingleton.elim x 0, submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at
     hx
 #align not_is_associated_prime_of_subsingleton not_isAssociatedPrime_of_subsingleton
+-/
 
 variable (R)
 
+/- warning: exists_le_is_associated_prime_of_is_noetherian_ring -> exists_le_isAssociatedPrime_of_isNoetherianRing is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (IsAssociatedPrime.{u1, u2} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) P)))
+but is expected to have type
+  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] (x : M), (Ne.{succ u1} M x (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M _inst_2)))))))) -> (Exists.{succ u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (fun (P : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) => And (IsAssociatedPrime.{u2, u1} R _inst_1 P M _inst_2 _inst_3) (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) x))) P)))
+Case conversion may be inaccurate. Consider using '#align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRingₓ'. -/
 theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R] (x : M)
     (hx : x ≠ 0) : ∃ P : Ideal R, IsAssociatedPrime P M ∧ (R ∙ x).annihilator ≤ P :=
   by
@@ -114,23 +150,43 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
 
 variable {R}
 
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+Case conversion may be inaccurate. Consider using '#align associated_primes.subset_of_injective associatedPrimes.subset_of_injectiveₓ'. -/
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun I h => h.map_of_injective f hf
 #align associated_primes.subset_of_injective associatedPrimes.subset_of_injective
 
+/- warning: linear_equiv.associated_primes.eq -> LinearEquiv.AssociatedPrimes.eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_equiv.associated_primes.eq LinearEquiv.AssociatedPrimes.eqₓ'. -/
 theorem LinearEquiv.AssociatedPrimes.eq (l : M ≃ₗ[R] M') :
     associatedPrimes R M = associatedPrimes R M' :=
   le_antisymm (associatedPrimes.subset_of_injective l l.Injective)
     (associatedPrimes.subset_of_injective l.symm l.symm.Injective)
 #align linear_equiv.associated_primes.eq LinearEquiv.AssociatedPrimes.eq
 
+#print associatedPrimes.eq_empty_of_subsingleton /-
 theorem associatedPrimes.eq_empty_of_subsingleton [Subsingleton M] : associatedPrimes R M = ∅ := by
   ext; simp only [Set.mem_empty_iff_false, iff_false_iff];
   apply not_isAssociatedPrime_of_subsingleton
 #align associated_primes.eq_empty_of_subsingleton associatedPrimes.eq_empty_of_subsingleton
+-/
 
 variable (R M)
 
+/- warning: associated_primes.nonempty -> associatedPrimes.nonempty is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] (M : Type.{u2}) [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_6 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_7 : Nontrivial.{u2} M], Set.Nonempty.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (associatedPrimes.{u1, u2} R _inst_1 M _inst_2 _inst_3)
+but is expected to have type
+  forall (R : Type.{u2}) [_inst_1 : CommRing.{u2} R] (M : Type.{u1}) [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_6 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] [_inst_7 : Nontrivial.{u1} M], Set.Nonempty.{u2} (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (associatedPrimes.{u2, u1} R _inst_1 M _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align associated_primes.nonempty associatedPrimes.nonemptyₓ'. -/
 theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
     (associatedPrimes R M).Nonempty :=
   by
@@ -141,6 +197,12 @@ theorem associatedPrimes.nonempty [IsNoetherianRing R] [Nontrivial M] :
 
 variable {R M}
 
+/- warning: is_associated_prime.annihilator_le -> IsAssociatedPrime.annihilator_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)], (IsAssociatedPrime.{u1, u2} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Submodule.annihilator.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {I : Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))} {M : Type.{u1}} [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)], (IsAssociatedPrime.{u2, u1} R _inst_1 I M _inst_2 _inst_3) -> (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Submodule.annihilator.{u2, u1} R M (CommRing.toCommSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) I)
+Case conversion may be inaccurate. Consider using '#align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_leₓ'. -/
 theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
     (⊤ : Submodule R M).annihilator ≤ I :=
   by
@@ -148,6 +210,7 @@ theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
   exact Submodule.annihilator_mono le_top
 #align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_le
 
+#print IsAssociatedPrime.eq_radical /-
 theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J (R ⧸ I)) :
     J = I.radical := by
   obtain ⟨hJ, x, e⟩ := h
@@ -167,7 +230,9 @@ theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J
     intro y hy
     exact e.mpr (I.mul_mem_left x hy)
 #align is_associated_prime.eq_radical IsAssociatedPrime.eq_radical
+-/
 
+#print associatedPrimes.eq_singleton_of_isPrimary /-
 theorem associatedPrimes.eq_singleton_of_isPrimary [IsNoetherianRing R] (hI : I.IsPrimary) :
     associatedPrimes R (R ⧸ I) = {I.radical} :=
   by
@@ -181,4 +246,5 @@ theorem associatedPrimes.eq_singleton_of_isPrimary [IsNoetherianRing R] (hI : I.
   rw [Ne.def, Ideal.Quotient.eq, sub_zero, ← Ideal.eq_top_iff_one]
   exact hI.1
 #align associated_primes.eq_singleton_of_is_primary associatedPrimes.eq_singleton_of_isPrimary
+-/

f0c8bf92

bump to nightly-2023-05-05-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

c17f6f14

Diff

@@ -4,15 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.associated_prime
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Span
 import Mathbin.RingTheory.Ideal.Operations
-import Mathbin.RingTheory.Finiteness
-import Mathbin.RingTheory.Localization.Ideal
-import Mathbin.RingTheory.Ideal.MinimalPrime
+import Mathbin.RingTheory.Ideal.QuotientOperations
+import Mathbin.RingTheory.Noetherian
 
 /-!

210657c4

bump to nightly-2023-04-02-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcb83fe7996142dfcfe7368d31304a9adc874a

a22ad38d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.associated_prime
-! leanprover-community/mathlib commit a652f6c3cd9ec14a56fe56229010f0fe0217a07c
+! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -109,7 +109,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
     rw [smul_comm, hc, smul_zero]
   have H₂ : (Submodule.span R {a • y}).annihilator ≠ ⊤ := by
     rwa [Ne.def, Submodule.annihilator_eq_top_iff, Submodule.span_singleton_eq_bot]
-  rwa [← h₃ (R ∙ a • y).annihilator ⟨l.trans H₁, H₂, _, rfl⟩ H₁,
+  rwa [H₁.eq_of_not_lt (h₃ (R ∙ a • y).annihilator ⟨l.trans H₁, H₂, _, rfl⟩),
     Submodule.mem_annihilator_span_singleton, smul_comm, smul_smul]
 #align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRing

a652f6c3

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f0c8bf92

chore: split out Ideal.IsPrimary (#12296)

This splits out a small but self-contained part of RingTheory.Ideal.Operations.

a1bf7622

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
 import Mathlib.LinearAlgebra.Span
-import Mathlib.RingTheory.Ideal.Operations
+import Mathlib.RingTheory.Ideal.IsPrimary
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.RingTheory.Noetherian

f0c8bf92

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -83,7 +83,7 @@ variable (R)
 theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R] (x : M)
     (hx : x ≠ 0) : ∃ P : Ideal R, IsAssociatedPrime P M ∧ (R ∙ x).annihilator ≤ P := by
   have : (R ∙ x).annihilator ≠ ⊤ := by
-    rwa [Ne.def, Ideal.eq_top_iff_one, Submodule.mem_annihilator_span_singleton, one_smul]
+    rwa [Ne, Ideal.eq_top_iff_one, Submodule.mem_annihilator_span_singleton, one_smul]
   obtain ⟨P, ⟨l, h₁, y, rfl⟩, h₃⟩ :=
     set_has_maximal_iff_noetherian.mpr H
       { P | (R ∙ x).annihilator ≤ P ∧ P ≠ ⊤ ∧ ∃ y : M, P = (R ∙ y).annihilator }
@@ -98,7 +98,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
     rw [Submodule.mem_annihilator_span_singleton] at hc ⊢
     rw [smul_comm, hc, smul_zero]
   have H₂ : (Submodule.span R {a • y}).annihilator ≠ ⊤ := by
-    rwa [Ne.def, Submodule.annihilator_eq_top_iff, Submodule.span_singleton_eq_bot]
+    rwa [Ne, Submodule.annihilator_eq_top_iff, Submodule.span_singleton_eq_bot]
   rwa [H₁.eq_of_not_lt (h₃ (R ∙ a • y).annihilator ⟨l.trans H₁, H₂, _, rfl⟩),
     Submodule.mem_annihilator_span_singleton, smul_comm, smul_smul]
 #align exists_le_is_associated_prime_of_is_noetherian_ring exists_le_isAssociatedPrime_of_isNoetherianRing
@@ -165,7 +165,7 @@ theorem associatedPrimes.eq_singleton_of_isPrimary [IsNoetherianRing R] (hI : I.
   rintro rfl
   haveI : Nontrivial (R ⧸ I) := by
     refine ⟨(Ideal.Quotient.mk I : _) 1, (Ideal.Quotient.mk I : _) 0, ?_⟩
-    rw [Ne.def, Ideal.Quotient.eq, sub_zero, ← Ideal.eq_top_iff_one]
+    rw [Ne, Ideal.Quotient.eq, sub_zero, ← Ideal.eq_top_iff_one]
     exact hI.1
   obtain ⟨a, ha⟩ := associatedPrimes.nonempty R (R ⧸ I)
   exact ha.eq_radical hI ▸ ha

f0c8bf92

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -49,7 +49,6 @@ def associatedPrimes : Set (Ideal R) :=
 #align associated_primes associatedPrimes
 
 variable {I J M R}
-
 variable {M' : Type*} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M := Iff.rfl

f0c8bf92

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -146,8 +146,8 @@ theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J
     apply hJ.1
     rwa [Submodule.span_singleton_eq_bot.mpr rfl, Submodule.annihilator_bot] at e
   obtain ⟨x, rfl⟩ := Ideal.Quotient.mkₐ_surjective R _ x
-  replace e : ∀ {y}, y ∈ J ↔ x * y ∈ I
-  · intro y
+  replace e : ∀ {y}, y ∈ J ↔ x * y ∈ I := by
+    intro y
     rw [e, Submodule.mem_annihilator_span_singleton, ← map_smul, smul_eq_mul, mul_comm,
       Ideal.Quotient.mkₐ_eq_mk, ← Ideal.Quotient.mk_eq_mk, Submodule.Quotient.mk_eq_zero]
   apply le_antisymm

f0c8bf92

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

@@ -34,7 +34,7 @@ Generalize this to a non-commutative setting once there are annihilator for non-
 -/
 
 
-variable {R : Type _} [CommRing R] (I J : Ideal R) (M : Type _) [AddCommGroup M] [Module R M]
+variable {R : Type*} [CommRing R] (I J : Ideal R) (M : Type*) [AddCommGroup M] [Module R M]
 
 /-- `IsAssociatedPrime I M` if the prime ideal `I` is the annihilator of some `x : M`. -/
 def IsAssociatedPrime : Prop :=
@@ -50,7 +50,7 @@ def associatedPrimes : Set (Ideal R) :=
 
 variable {I J M R}
 
-variable {M' : Type _} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
+variable {M' : Type*} [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M')
 
 theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPrime I M := Iff.rfl
 #align associate_primes.mem_iff AssociatePrimes.mem_iff

f0c8bf92

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.ideal.associated_prime
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Span
 import Mathlib.RingTheory.Ideal.Operations
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.RingTheory.Noetherian
 
+#align_import ring_theory.ideal.associated_prime from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 
 # Associated primes of a module

f0c8bf92

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

@@ -99,7 +99,7 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
   rw [Submodule.mem_annihilator_span_singleton] at ha hab
   have H₁ : (R ∙ y).annihilator ≤ (R ∙ a • y).annihilator := by
     intro c hc
-    rw [Submodule.mem_annihilator_span_singleton] at hc⊢
+    rw [Submodule.mem_annihilator_span_singleton] at hc ⊢
     rw [smul_comm, hc, smul_zero]
   have H₂ : (Submodule.span R {a • y}).annihilator ≠ ⊤ := by
     rwa [Ne.def, Submodule.annihilator_eq_top_iff, Submodule.span_singleton_eq_bot]

f0c8bf92

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -60,7 +60,6 @@ theorem AssociatePrimes.mem_iff : I ∈ associatedPrimes R M ↔ IsAssociatedPri
 
 theorem IsAssociatedPrime.isPrime (h : IsAssociatedPrime I M) : I.IsPrime := h.1
 #align is_associated_prime.is_prime IsAssociatedPrime.isPrime
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Function.Injective f) :
     IsAssociatedPrime I M' := by
   obtain ⟨x, rfl⟩ := h.2
@@ -70,7 +69,6 @@ theorem IsAssociatedPrime.map_of_injective (h : IsAssociatedPrime I M) (hf : Fun
     map_smul, ← f.map_zero, hf.eq_iff]
 #align is_associated_prime.map_of_injective IsAssociatedPrime.map_of_injective
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem LinearEquiv.isAssociatedPrime_iff (l : M ≃ₗ[R] M') :
     IsAssociatedPrime I M ↔ IsAssociatedPrime I M' :=
   ⟨fun h => h.map_of_injective l l.injective,
@@ -111,12 +109,10 @@ theorem exists_le_isAssociatedPrime_of_isNoetherianRing [H : IsNoetherianRing R]
 
 variable {R}
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem associatedPrimes.subset_of_injective (hf : Function.Injective f) :
     associatedPrimes R M ⊆ associatedPrimes R M' := fun _I h => h.map_of_injective f hf
 #align associated_primes.subset_of_injective associatedPrimes.subset_of_injective
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem LinearEquiv.AssociatedPrimes.eq (l : M ≃ₗ[R] M') :
     associatedPrimes R M = associatedPrimes R M' :=
   le_antisymm (associatedPrimes.subset_of_injective l l.injective)
@@ -145,7 +141,6 @@ theorem IsAssociatedPrime.annihilator_le (h : IsAssociatedPrime I M) :
   exact Submodule.annihilator_mono le_top
 #align is_associated_prime.annihilator_le IsAssociatedPrime.annihilator_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: added
 theorem IsAssociatedPrime.eq_radical (hI : I.IsPrimary) (h : IsAssociatedPrime J (R ⧸ I)) :
     J = I.radical := by
   obtain ⟨hJ, x, e⟩ := h

f0c8bf92

feat port : RingTheory.Ideal.AssociatedPrime (#3810)

4a20b63f

`ring_theory.ideal.associated_prime` ⟷ `Mathlib.RingTheory.Ideal.AssociatedPrime`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

ring_theory.ideal.associated_prime ⟷ Mathlib.RingTheory.Ideal.AssociatedPrime

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

`ring_theory.ideal.associated_prime` ⟷ `Mathlib.RingTheory.Ideal.AssociatedPrime`