ring_theory.ideal.minimal_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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4280f5f3

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -106,7 +106,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
@@ -139,7 +139,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
@@ -173,7 +173,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_minimalPrimes_comap_eq /-
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=

4280f5f3

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -62,7 +62,7 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
       OrderDual.toDual J ≤ m ∧ ∀ z ∈ {p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ p}, m ≤ z → z = m
     by
     obtain ⟨p, h₁, h₂, h₃⟩ := this
-    simp_rw [← @eq_comm _ p] at h₃ 
+    simp_rw [← @eq_comm _ p] at h₃
     exact ⟨p, ⟨h₁, fun a b c => (h₃ a b c).le⟩, h₂⟩
   apply zorn_nonempty_partialOrder₀
   swap; · refine' ⟨show J.is_prime by infer_instance, e⟩

4280f5f3

bump to nightly-2023-10-04-06

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

7bd6a14d

Diff

@@ -188,8 +188,8 @@ theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
 #align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eq
 -/
 
-#print Ideal.mimimal_primes_comap_of_surjective /-
-theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
+#print Ideal.minimal_primes_comap_of_surjective /-
+theorem Ideal.minimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     {I J : Ideal S} (h : J ∈ I.minimalPrimes) : J.comap f ∈ (I.comap f).minimalPrimes :=
   by
   haveI := h.1.1
@@ -201,7 +201,7 @@ theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.
   apply h.2 _ _
   · exact ⟨Ideal.map_isPrime_of_surjective hf this, Ideal.le_map_of_comap_le_of_surjective f hf e₁⟩
   · exact Ideal.map_le_of_le_comap e₂
-#align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjective
+#align ideal.mimimal_primes_comap_of_surjective Ideal.minimal_primes_comap_of_surjective
 -/
 
 #print Ideal.comap_minimalPrimes_eq_of_surjective /-
@@ -211,7 +211,7 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
   ext J
   constructor
   · intro H; obtain ⟨p, h, rfl⟩ := Ideal.exists_minimalPrimes_comap_eq f J H; exact ⟨p, h, rfl⟩
-  · rintro ⟨J, hJ, rfl⟩; exact Ideal.mimimal_primes_comap_of_surjective hf hJ
+  · rintro ⟨J, hJ, rfl⟩; exact Ideal.minimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
 -/

4280f5f3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.RingTheory.Localization.AtPrime
-import Mathbin.Order.Minimal
+import RingTheory.Localization.AtPrime
+import Order.Minimal
 
 #align_import ring_theory.ideal.minimal_prime from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 
@@ -106,7 +106,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
@@ -139,7 +139,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
@@ -173,7 +173,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_minimalPrimes_comap_eq /-
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=

4280f5f3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 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.minimal_prime
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Localization.AtPrime
 import Mathbin.Order.Minimal
 
+#align_import ring_theory.ideal.minimal_prime from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 
 # Minimal primes
@@ -109,7 +106,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
@@ -142,7 +139,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_comap_eq_of_mem_minimalPrimes /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
@@ -176,7 +173,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 #print Ideal.exists_minimalPrimes_comap_eq /-
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=

4280f5f3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,6 +57,7 @@ def minimalPrimes (R : Type _) [CommRing R] : Set (Ideal R) :=
 
 variable {I J}
 
+#print Ideal.exists_minimalPrimes_le /-
 theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.minimalPrimes, p ≤ J :=
   by
   suffices
@@ -77,6 +78,7 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
     rw [OrderDual.le_toDual]
     exact sInf_le hz
 #align ideal.exists_minimal_primes_le Ideal.exists_minimalPrimes_le
+-/
 
 #print Ideal.radical_minimalPrimes /-
 @[simp]
@@ -89,6 +91,7 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
 -/
 
+#print Ideal.sInf_minimalPrimes /-
 @[simp]
 theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
   by
@@ -104,8 +107,10 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
     intro I hI
     exact hI.1.symm
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+#print Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
     ∃ p' : Ideal S, p'.IsPrime ∧ p'.comap f = p :=
@@ -135,8 +140,10 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   apply IsLocalization.map_units _ (show p.prime_compl from ⟨x, h⟩)
   infer_instance
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+#print Ideal.exists_comap_eq_of_mem_minimalPrimes /-
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
   by
@@ -167,8 +174,10 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
     · refine' (Ideal.comap_mono hq').trans _; rw [Ideal.comap_map_of_surjective]
       exacts [sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+#print Ideal.exists_minimalPrimes_comap_eq /-
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=
   by
@@ -180,7 +189,9 @@ theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
   have := (Ideal.comap_mono hq').trans_eq h₃
   exact (H.2 ⟨inferInstance, Ideal.comap_mono hq.1.2⟩ this).antisymm this
 #align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eq
+-/
 
+#print Ideal.mimimal_primes_comap_of_surjective /-
 theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     {I J : Ideal S} (h : J ∈ I.minimalPrimes) : J.comap f ∈ (I.comap f).minimalPrimes :=
   by
@@ -194,7 +205,9 @@ theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.
   · exact ⟨Ideal.map_isPrime_of_surjective hf this, Ideal.le_map_of_comap_le_of_surjective f hf e₁⟩
   · exact Ideal.map_le_of_le_comap e₂
 #align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjective
+-/
 
+#print Ideal.comap_minimalPrimes_eq_of_surjective /-
 theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     (I : Ideal S) : (I.comap f).minimalPrimes = Ideal.comap f '' I.minimalPrimes :=
   by
@@ -203,12 +216,15 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
   · intro H; obtain ⟨p, h, rfl⟩ := Ideal.exists_minimalPrimes_comap_eq f J H; exact ⟨p, h, rfl⟩
   · rintro ⟨J, hJ, rfl⟩; exact Ideal.mimimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
+-/
 
+#print Ideal.minimalPrimes_eq_comap /-
 theorem Ideal.minimalPrimes_eq_comap :
     I.minimalPrimes = Ideal.comap I.Quotient.mk '' minimalPrimes (R ⧸ I) := by
   rw [minimalPrimes, ← Ideal.comap_minimalPrimes_eq_of_surjective Ideal.Quotient.mk_surjective, ←
     RingHom.ker_eq_comap_bot, Ideal.mk_ker]
 #align ideal.minimal_primes_eq_comap Ideal.minimalPrimes_eq_comap
+-/
 
 #print Ideal.minimalPrimes_eq_subsingleton /-
 theorem Ideal.minimalPrimes_eq_subsingleton (hI : I.IsPrimary) : I.minimalPrimes = {I.radical} :=

4280f5f3

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -105,7 +105,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
     exact hI.1.symm
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
     ∃ p' : Ideal S, p'.IsPrime ∧ p'.comap f = p :=
@@ -136,7 +136,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   infer_instance
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
   by
@@ -168,7 +168,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       exacts [sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=
   by

4280f5f3

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -43,7 +43,7 @@ variable {R S : Type _} [CommRing R] [CommRing S] (I J : Ideal R)
 #print Ideal.minimalPrimes /-
 /-- `I.minimal_primes` is the set of ideals that are minimal primes over `I`. -/
 def Ideal.minimalPrimes : Set (Ideal R) :=
-  minimals (· ≤ ·) { p | p.IsPrime ∧ I ≤ p }
+  minimals (· ≤ ·) {p | p.IsPrime ∧ I ≤ p}
 #align ideal.minimal_primes Ideal.minimalPrimes
 -/
 
@@ -60,8 +60,8 @@ variable {I J}
 theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.minimalPrimes, p ≤ J :=
   by
   suffices
-    ∃ m ∈ { p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ OrderDual.ofDual p },
-      OrderDual.toDual J ≤ m ∧ ∀ z ∈ { p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ p }, m ≤ z → z = m
+    ∃ m ∈ {p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ OrderDual.ofDual p},
+      OrderDual.toDual J ≤ m ∧ ∀ z ∈ {p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ p}, m ≤ z → z = m
     by
     obtain ⟨p, h₁, h₂, h₃⟩ := this
     simp_rw [← @eq_comm _ p] at h₃ 
@@ -114,7 +114,8 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   have : Nontrivial (Localization (Submonoid.map f p.prime_compl)) :=
     by
     refine' ⟨⟨1, 0, _⟩⟩
-    convert(IsLocalization.map_injective_of_injective p.prime_compl (Localization.AtPrime p)
+    convert
+      (IsLocalization.map_injective_of_injective p.prime_compl (Localization.AtPrime p)
             (Localization <| p.prime_compl.map f) hf).Ne
         one_ne_zero
     · rw [map_one]; · rw [map_zero]

4280f5f3

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -64,7 +64,7 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
       OrderDual.toDual J ≤ m ∧ ∀ z ∈ { p : (Ideal R)ᵒᵈ | Ideal.IsPrime p ∧ I ≤ p }, m ≤ z → z = m
     by
     obtain ⟨p, h₁, h₂, h₃⟩ := this
-    simp_rw [← @eq_comm _ p] at h₃
+    simp_rw [← @eq_comm _ p] at h₃ 
     exact ⟨p, ⟨h₁, fun a b c => (h₃ a b c).le⟩, h₂⟩
   apply zorn_nonempty_partialOrder₀
   swap; · refine' ⟨show J.is_prime by infer_instance, e⟩
@@ -95,7 +95,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
   rw [I.radical_eq_Inf]
   apply le_antisymm
   · intro x hx
-    rw [Ideal.mem_sInf] at hx⊢
+    rw [Ideal.mem_sInf] at hx ⊢
     rintro J ⟨e, hJ⟩
     skip
     obtain ⟨p, hp, hp'⟩ := Ideal.exists_minimalPrimes_le e
@@ -164,7 +164,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
     apply H.2
     · refine' ⟨inferInstance, (ideal.mk_ker.trans e).symm.trans_le (Ideal.comap_mono bot_le)⟩
     · refine' (Ideal.comap_mono hq').trans _; rw [Ideal.comap_map_of_surjective]
-      exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
+      exacts [sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/

4280f5f3

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -57,12 +57,6 @@ def minimalPrimes (R : Type _) [CommRing R] : Set (Ideal R) :=
 
 variable {I J}
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_minimal_primes_le Ideal.exists_minimalPrimes_leₓ'. -/
 theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.minimalPrimes, p ≤ J :=
   by
   suffices
@@ -95,12 +89,6 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
 -/
 
-/- warning: ideal.Inf_minimal_primes -> Ideal.sInf_minimalPrimes 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))}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.minimalPrimes.{u1} R _inst_1 I)) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (InfSet.sInf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instInfSetSubmodule.{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)))) (Ideal.minimalPrimes.{u1} R _inst_1 I)) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I)
-Case conversion may be inaccurate. Consider using '#align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimesₓ'. -/
 @[simp]
 theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
   by
@@ -117,12 +105,6 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
     exact hI.1.symm
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
@@ -153,12 +135,6 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   infer_instance
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimesₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
@@ -191,12 +167,6 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=
@@ -210,12 +180,6 @@ theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
   exact (H.2 ⟨inferInstance, Ideal.comap_mono hq.1.2⟩ this).antisymm this
 #align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eq
 
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-Case conversion may be inaccurate. Consider using '#align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjectiveₓ'. -/
 theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     {I J : Ideal S} (h : J ∈ I.minimalPrimes) : J.comap f ∈ (I.comap f).minimalPrimes :=
   by
@@ -230,12 +194,6 @@ theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.
   · exact Ideal.map_le_of_le_comap e₂
 #align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjective
 
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-Case conversion may be inaccurate. Consider using '#align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjectiveₓ'. -/
 theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     (I : Ideal S) : (I.comap f).minimalPrimes = Ideal.comap f '' I.minimalPrimes :=
   by
@@ -245,12 +203,6 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
   · rintro ⟨J, hJ, rfl⟩; exact Ideal.mimimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
 
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-Case conversion may be inaccurate. Consider using '#align ideal.minimal_primes_eq_comap Ideal.minimalPrimes_eq_comapₓ'. -/
 theorem Ideal.minimalPrimes_eq_comap :
     I.minimalPrimes = Ideal.comap I.Quotient.mk '' minimalPrimes (R ⧸ I) := by
   rw [minimalPrimes, ← Ideal.comap_minimalPrimes_eq_of_surjective Ideal.Quotient.mk_surjective, ←

4280f5f3

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -73,16 +73,12 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
     simp_rw [← @eq_comm _ p] at h₃
     exact ⟨p, ⟨h₁, fun a b c => (h₃ a b c).le⟩, h₂⟩
   apply zorn_nonempty_partialOrder₀
-  swap
-  · refine' ⟨show J.is_prime by infer_instance, e⟩
+  swap; · refine' ⟨show J.is_prime by infer_instance, e⟩
   rintro (c : Set (Ideal R)) hc hc' J' hJ'
   refine'
     ⟨OrderDual.toDual (Inf c),
       ⟨Ideal.sInf_isPrime_of_isChain ⟨J', hJ'⟩ hc'.symm fun x hx => (hc hx).1, _⟩, _⟩
-  · rw [OrderDual.ofDual_toDual]
-    convert le_sInf _
-    intro x hx
-    exact (hc hx).2
+  · rw [OrderDual.ofDual_toDual]; convert le_sInf _; intro x hx; exact (hc hx).2
   · rintro z hz
     rw [OrderDual.le_toDual]
     exact sInf_le hz
@@ -139,8 +135,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     convert(IsLocalization.map_injective_of_injective p.prime_compl (Localization.AtPrime p)
             (Localization <| p.prime_compl.map f) hf).Ne
         one_ne_zero
-    · rw [map_one]
-    · rw [map_zero]
+    · rw [map_one]; · rw [map_zero]
   obtain ⟨M, hM⟩ := Ideal.exists_maximal (Localization (Submonoid.map f p.prime_compl))
   skip
   refine' ⟨M.comap (algebraMap S <| Localization (Submonoid.map f p.prime_compl)), inferInstance, _⟩
@@ -170,14 +165,8 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
   by
   haveI := H.1.1
   let f' := I.Quotient.mk.comp f
-  have e : (I.Quotient.mk.comp f).ker = I.comap f :=
-    by
-    ext1
-    exact Submodule.Quotient.mk_eq_zero _
-  have : (I.Quotient.mk.comp f).ker.Quotient.mk.ker ≤ p :=
-    by
-    rw [Ideal.mk_ker, e]
-    exact H.1.2
+  have e : (I.Quotient.mk.comp f).ker = I.comap f := by ext1; exact Submodule.Quotient.mk_eq_zero _
+  have : (I.Quotient.mk.comp f).ker.Quotient.mk.ker ≤ p := by rw [Ideal.mk_ker, e]; exact H.1.2
   obtain ⟨p', hp₁, hp₂⟩ :=
     Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
       (I.Quotient.mk.comp f).ker_lift_injective (p.map (I.Quotient.mk.comp f).ker.Quotient.mk) _
@@ -189,8 +178,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
         Ideal.Quotient.mk_surjective,
       eq_comm, sup_eq_left]
   refine' ⟨⟨_, bot_le⟩, _⟩
-  · apply Ideal.map_isPrime_of_surjective _ this
-    exact Ideal.Quotient.mk_surjective
+  · apply Ideal.map_isPrime_of_surjective _ this; exact Ideal.Quotient.mk_surjective
   · rintro q ⟨hq, -⟩ hq'
     rw [←
       Ideal.map_comap_of_surjective (I.Quotient.mk.comp f).ker.Quotient.mk
@@ -199,8 +187,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
     skip
     apply H.2
     · refine' ⟨inferInstance, (ideal.mk_ker.trans e).symm.trans_le (Ideal.comap_mono bot_le)⟩
-    · refine' (Ideal.comap_mono hq').trans _
-      rw [Ideal.comap_map_of_surjective]
+    · refine' (Ideal.comap_mono hq').trans _; rw [Ideal.comap_map_of_surjective]
       exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
@@ -254,11 +241,8 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
   by
   ext J
   constructor
-  · intro H
-    obtain ⟨p, h, rfl⟩ := Ideal.exists_minimalPrimes_comap_eq f J H
-    exact ⟨p, h, rfl⟩
-  · rintro ⟨J, hJ, rfl⟩
-    exact Ideal.mimimal_primes_comap_of_surjective hf hJ
+  · intro H; obtain ⟨p, h, rfl⟩ := Ideal.exists_minimalPrimes_comap_eq f J H; exact ⟨p, h, rfl⟩
+  · rintro ⟨J, hJ, rfl⟩; exact Ideal.mimimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
 
 /- warning: ideal.minimal_primes_eq_comap -> Ideal.minimalPrimes_eq_comap is a dubious translation:
@@ -293,8 +277,7 @@ theorem Ideal.minimalPrimes_eq_subsingleton_self [I.IsPrime] : I.minimalPrimes =
   ext J
   constructor
   · exact fun H => (H.2 ⟨inferInstance, rfl.le⟩ H.1.2).antisymm H.1.2
-  · rintro (rfl : J = I)
-    refine' ⟨⟨inferInstance, rfl.le⟩, fun _ h _ => h.2⟩
+  · rintro (rfl : J = I); refine' ⟨⟨inferInstance, rfl.le⟩, fun _ h _ => h.2⟩
 #align ideal.minimal_primes_eq_subsingleton_self Ideal.minimalPrimes_eq_subsingleton_self
 -/

4280f5f3

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

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.minimal_prime
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Order.Minimal
 
 # Minimal primes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We provide various results concerning the minimal primes above an ideal
 
 ## Main results

70fd9563

bump to nightly-2023-05-21-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

3dfd63e0

Diff

@@ -37,19 +37,29 @@ section
 
 variable {R S : Type _} [CommRing R] [CommRing S] (I J : Ideal R)
 
+#print Ideal.minimalPrimes /-
 /-- `I.minimal_primes` is the set of ideals that are minimal primes over `I`. -/
 def Ideal.minimalPrimes : Set (Ideal R) :=
   minimals (· ≤ ·) { p | p.IsPrime ∧ I ≤ p }
 #align ideal.minimal_primes Ideal.minimalPrimes
+-/
 
+#print minimalPrimes /-
 /-- `minimal_primes R` is the set of minimal primes of `R`.
 This is defined as `ideal.minimal_primes ⊥`. -/
 def minimalPrimes (R : Type _) [CommRing R] : Set (Ideal R) :=
   Ideal.minimalPrimes ⊥
 #align minimal_primes minimalPrimes
+-/
 
 variable {I J}
 
+/- warning: ideal.exists_minimal_primes_le -> Ideal.exists_minimalPrimes_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))} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} [_inst_3 : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) J], (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) I J) -> (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))) => Exists.{0} (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)))) p (Ideal.minimalPrimes.{u1} R _inst_1 I)) (fun (H : 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)))) p (Ideal.minimalPrimes.{u1} R _inst_1 I)) => LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p J)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} [_inst_3 : Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) J], (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))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{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)))))))) I J) -> (Exists.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (Membership.mem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p (Ideal.minimalPrimes.{u1} R _inst_1 I)) (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))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{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)))))))) p J)))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_minimal_primes_le Ideal.exists_minimalPrimes_leₓ'. -/
 theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.minimalPrimes, p ≤ J :=
   by
   suffices
@@ -75,6 +85,7 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
     exact sInf_le hz
 #align ideal.exists_minimal_primes_le Ideal.exists_minimalPrimes_le
 
+#print Ideal.radical_minimalPrimes /-
 @[simp]
 theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes :=
   by
@@ -83,7 +94,14 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
   ext p
   exact ⟨fun ⟨a, b⟩ => ⟨a, ideal.le_radical.trans b⟩, fun ⟨a, b⟩ => ⟨a, a.radical_le_iff.mpr b⟩⟩
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
+-/
 
+/- warning: ideal.Inf_minimal_primes -> Ideal.sInf_minimalPrimes 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))}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.minimalPrimes.{u1} R _inst_1 I)) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (InfSet.sInf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instInfSetSubmodule.{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)))) (Ideal.minimalPrimes.{u1} R _inst_1 I)) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I)
+Case conversion may be inaccurate. Consider using '#align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimesₓ'. -/
 @[simp]
 theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
   by
@@ -100,6 +118,12 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
     exact hI.1.symm
 #align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 
+/- warning: ideal.exists_comap_eq_of_mem_minimal_primes_of_injective -> Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))}, (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f)) -> (forall (p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (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)))) p (minimalPrimes.{u1} R _inst_1)) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (p' : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => And (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p') (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f p') p))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] {f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))}, (Function.Injective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) f)) -> (forall (p : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))), (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)))) p (minimalPrimes.{u2} R _inst_1)) -> (Exists.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (fun (p' : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) => And (Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) p') (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f p') p))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injectiveₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
@@ -131,6 +155,12 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   infer_instance
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 
+/- warning: ideal.exists_comap_eq_of_mem_minimal_primes -> Ideal.exists_comap_eq_of_mem_minimalPrimes is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (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)))) p (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (p' : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => And (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p') (And (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) I p') (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f p') p))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Membership.mem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))) -> (Exists.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (fun (p' : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) => And (Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) p') (And (LE.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))))) I p') (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f p') p))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimesₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
@@ -171,6 +201,12 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
+/- warning: ideal.exists_minimal_primes_comap_eq -> Ideal.exists_minimalPrimes_comap_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (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)))) p (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (p' : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => Exists.{0} (Membership.Mem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Set.hasMem.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) p' (Ideal.minimalPrimes.{u2} S _inst_2 I)) (fun (H : Membership.Mem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Set.hasMem.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) p' (Ideal.minimalPrimes.{u2} S _inst_2 I)) => Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f p') p)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Membership.mem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))) -> (Exists.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (fun (p' : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) => And (Membership.mem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Set.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (Set.instMembershipSet.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) p' (Ideal.minimalPrimes.{u2} S _inst_2 I)) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f p') p)))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eqₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=
@@ -184,6 +220,12 @@ theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
   exact (H.2 ⟨inferInstance, Ideal.comap_mono hq.1.2⟩ this).antisymm this
 #align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eq
 
+/- warning: ideal.mimimal_primes_comap_of_surjective -> Ideal.mimimal_primes_comap_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))}, (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f)) -> (forall {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))}, (Membership.Mem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Set.hasMem.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) J (Ideal.minimalPrimes.{u2} S _inst_2 I)) -> (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)))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f J) (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] {f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))}, (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) f)) -> (forall {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} {J : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))}, (Membership.mem.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Set.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (Set.instMembershipSet.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) J (Ideal.minimalPrimes.{u1} S _inst_2 I)) -> (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)))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f J) (Ideal.minimalPrimes.{u2} R _inst_1 (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f I))))
+Case conversion may be inaccurate. Consider using '#align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjectiveₓ'. -/
 theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     {I J : Ideal S} (h : J ∈ I.minimalPrimes) : J.comap f ∈ (I.comap f).minimalPrimes :=
   by
@@ -198,6 +240,12 @@ theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.
   · exact Ideal.map_le_of_le_comap e₂
 #align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjective
 
+/- warning: ideal.comap_minimal_primes_eq_of_surjective -> Ideal.comap_minimalPrimes_eq_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))}, (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f)) -> (forall (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))), Eq.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.minimalPrimes.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Set.image.{u2, u1} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f) (Ideal.minimalPrimes.{u2} S _inst_2 I)))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] {f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))}, (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))) f)) -> (forall (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))), Eq.{succ u2} (Set.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Ideal.minimalPrimes.{u2} R _inst_1 (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f I)) (Set.image.{u1, u2} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f) (Ideal.minimalPrimes.{u1} S _inst_2 I)))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjectiveₓ'. -/
 theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     (I : Ideal S) : (I.comap f).minimalPrimes = Ideal.comap f '' I.minimalPrimes :=
   by
@@ -210,12 +258,19 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
     exact Ideal.mimimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
 
+/- warning: ideal.minimal_primes_eq_comap -> Ideal.minimalPrimes_eq_comap 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))}, Eq.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.minimalPrimes.{u1} R _inst_1 I) (Set.image.{u1, u1} (Ideal.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I)))) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))) (RingHom.ringHomClass.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))))) (Ideal.Quotient.mk.{u1} R _inst_1 I)) (minimalPrimes.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Eq.{succ u1} (Set.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.minimalPrimes.{u1} R _inst_1 I) (Set.image.{u1, u1} (Ideal.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I)))) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I))))) (Ideal.Quotient.mk.{u1} R _inst_1 I)) (minimalPrimes.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) I) (Ideal.Quotient.commRing.{u1} R _inst_1 I)))
+Case conversion may be inaccurate. Consider using '#align ideal.minimal_primes_eq_comap Ideal.minimalPrimes_eq_comapₓ'. -/
 theorem Ideal.minimalPrimes_eq_comap :
     I.minimalPrimes = Ideal.comap I.Quotient.mk '' minimalPrimes (R ⧸ I) := by
   rw [minimalPrimes, ← Ideal.comap_minimalPrimes_eq_of_surjective Ideal.Quotient.mk_surjective, ←
     RingHom.ker_eq_comap_bot, Ideal.mk_ker]
 #align ideal.minimal_primes_eq_comap Ideal.minimalPrimes_eq_comap
 
+#print Ideal.minimalPrimes_eq_subsingleton /-
 theorem Ideal.minimalPrimes_eq_subsingleton (hI : I.IsPrimary) : I.minimalPrimes = {I.radical} :=
   by
   ext J
@@ -227,7 +282,9 @@ theorem Ideal.minimalPrimes_eq_subsingleton (hI : I.IsPrimary) : I.minimalPrimes
   · rintro (rfl : J = I.radical)
     exact ⟨⟨Ideal.isPrime_radical hI, Ideal.le_radical⟩, fun _ H _ => H.1.radical_le_iff.mpr H.2⟩
 #align ideal.minimal_primes_eq_subsingleton Ideal.minimalPrimes_eq_subsingleton
+-/
 
+#print Ideal.minimalPrimes_eq_subsingleton_self /-
 theorem Ideal.minimalPrimes_eq_subsingleton_self [I.IsPrime] : I.minimalPrimes = {I} :=
   by
   ext J
@@ -236,6 +293,7 @@ theorem Ideal.minimalPrimes_eq_subsingleton_self [I.IsPrime] : I.minimalPrimes =
   · rintro (rfl : J = I)
     refine' ⟨⟨inferInstance, rfl.le⟩, fun _ h _ => h.2⟩
 #align ideal.minimal_primes_eq_subsingleton_self Ideal.minimalPrimes_eq_subsingleton_self
+-/
 
 end

70fd9563

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -65,14 +65,14 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
   rintro (c : Set (Ideal R)) hc hc' J' hJ'
   refine'
     ⟨OrderDual.toDual (Inf c),
-      ⟨Ideal.infₛ_isPrime_of_isChain ⟨J', hJ'⟩ hc'.symm fun x hx => (hc hx).1, _⟩, _⟩
+      ⟨Ideal.sInf_isPrime_of_isChain ⟨J', hJ'⟩ hc'.symm fun x hx => (hc hx).1, _⟩, _⟩
   · rw [OrderDual.ofDual_toDual]
-    convert le_infₛ _
+    convert le_sInf _
     intro x hx
     exact (hc hx).2
   · rintro z hz
     rw [OrderDual.le_toDual]
-    exact infₛ_le hz
+    exact sInf_le hz
 #align ideal.exists_minimal_primes_le Ideal.exists_minimalPrimes_le
 
 @[simp]
@@ -85,20 +85,20 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
 
 @[simp]
-theorem Ideal.infₛ_minimalPrimes : infₛ I.minimalPrimes = I.radical :=
+theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical :=
   by
   rw [I.radical_eq_Inf]
   apply le_antisymm
   · intro x hx
-    rw [Ideal.mem_infₛ] at hx⊢
+    rw [Ideal.mem_sInf] at hx⊢
     rintro J ⟨e, hJ⟩
     skip
     obtain ⟨p, hp, hp'⟩ := Ideal.exists_minimalPrimes_le e
     exact hp' (hx hp)
-  · apply infₛ_le_infₛ _
+  · apply sInf_le_sInf _
     intro I hI
     exact hI.1.symm
-#align ideal.Inf_minimal_primes Ideal.infₛ_minimalPrimes
+#align ideal.Inf_minimal_primes Ideal.sInf_minimalPrimes
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}

70fd9563

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -109,8 +109,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   have : Nontrivial (Localization (Submonoid.map f p.prime_compl)) :=
     by
     refine' ⟨⟨1, 0, _⟩⟩
-    convert
-      (IsLocalization.map_injective_of_injective p.prime_compl (Localization.AtPrime p)
+    convert(IsLocalization.map_injective_of_injective p.prime_compl (Localization.AtPrime p)
             (Localization <| p.prime_compl.map f) hf).Ne
         one_ne_zero
     · rw [map_one]

70fd9563

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -100,7 +100,7 @@ theorem Ideal.infₛ_minimalPrimes : infₛ I.minimalPrimes = I.radical :=
     exact hI.1.symm
 #align ideal.Inf_minimal_primes Ideal.infₛ_minimalPrimes
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » minimal_primes[minimal_primes] R) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
     (hf : Function.Injective f) (p) (_ : p ∈ minimalPrimes R) :
     ∃ p' : Ideal S, p'.IsPrime ∧ p'.comap f = p :=
@@ -132,7 +132,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   infer_instance
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p :=
   by
@@ -172,7 +172,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (p «expr ∈ » (I.comap f).minimal_primes) -/
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
     (_ : p ∈ (I.comap f).minimalPrimes) : ∃ p' ∈ I.minimalPrimes, Ideal.comap f p' = p :=
   by

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: split out Ideal.IsPrimary (#12296)

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

a1bf7622

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
+import Mathlib.RingTheory.Ideal.IsPrimary
 import Mathlib.RingTheory.Localization.AtPrime
 import Mathlib.Order.Minimal

70fd9563

feat(RingTheory/Localization): add facts about localization at minimal prime ideals (#11201)

Show that localization at minimal primes results in rings with only a single prime ideal, implying that every non-unit element is nilpotent.

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

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: uniwuni <95649083+uniwuni@users.noreply.github.com>

415f2144

Diff

@@ -25,7 +25,8 @@ We provide various results concerning the minimal primes above an ideal
   preimage of some minimal prime over `I`.
 - `Ideal.minimalPrimes_eq_comap`: The minimal primes over `I` are precisely the preimages of
   minimal primes of `R ⧸ I`.
-
+- `Localization.AtPrime.prime_unique_of_minimal`: When localizing at a minimal prime ideal `I`,
+  the resulting ring only has a single prime ideal.
 
 -/
 
@@ -221,3 +222,31 @@ theorem Ideal.minimalPrimes_eq_subsingleton_self [I.IsPrime] : I.minimalPrimes =
 #align ideal.minimal_primes_eq_subsingleton_self Ideal.minimalPrimes_eq_subsingleton_self
 
 end
+
+namespace Localization.AtPrime
+
+variable {R : Type*} [CommSemiring R] {I : Ideal R} [hI : I.IsPrime] (hMin : I ∈ minimalPrimes R)
+
+theorem _root_.IsLocalization.AtPrime.prime_unique_of_minimal {S} [CommSemiring S] [Algebra R S]
+    [IsLocalization.AtPrime S I] {J K : Ideal S} [J.IsPrime] [K.IsPrime] : J = K :=
+  haveI : Subsingleton {i : Ideal R // i.IsPrime ∧ i ≤ I} := ⟨fun i₁ i₂ ↦ Subtype.ext <| by
+    rw [minimalPrimes_eq_minimals] at hMin
+    rw [← eq_of_mem_minimals hMin i₁.2.1 i₁.2.2, ← eq_of_mem_minimals hMin i₂.2.1 i₂.2.2]⟩
+  Subtype.ext_iff.mp <| (IsLocalization.AtPrime.orderIsoOfPrime S I).injective
+    (a₁ := ⟨J, ‹_›⟩) (a₂ := ⟨K, ‹_›⟩) (Subsingleton.elim _ _)
+
+theorem prime_unique_of_minimal (J : Ideal (Localization I.primeCompl)) [J.IsPrime] :
+    J = LocalRing.maximalIdeal (Localization I.primeCompl) :=
+  IsLocalization.AtPrime.prime_unique_of_minimal hMin
+
+theorem nilpotent_iff_mem_maximal_of_minimal {x : _} :
+    IsNilpotent x ↔ x ∈ LocalRing.maximalIdeal (Localization I.primeCompl) := by
+  rw [nilpotent_iff_mem_prime]
+  exact ⟨(· (LocalRing.maximalIdeal _) (Ideal.IsMaximal.isPrime' _)), fun _ J _ =>
+    by simpa [prime_unique_of_minimal hMin J]⟩
+
+theorem nilpotent_iff_not_unit_of_minimal {x : Localization I.primeCompl} :
+    IsNilpotent x ↔ x ∈ nonunits _ := by
+  simpa only [← LocalRing.mem_maximalIdeal] using nilpotent_iff_mem_maximal_of_minimal hMin
+
+end Localization.AtPrime

70fd9563

chore: remove unused tactics (#11351)

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

b99084a9

Diff

@@ -75,7 +75,6 @@ theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.mi
 @[simp]
 theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes := by
   rw [Ideal.minimalPrimes, Ideal.minimalPrimes]
-  congr
   ext p
   refine' ⟨_, _⟩ <;> rintro ⟨⟨a, ha⟩, b⟩
   · refine' ⟨⟨a, a.radical_le_iff.1 ha⟩, _⟩

70fd9563

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -218,7 +218,7 @@ theorem Ideal.minimalPrimes_eq_subsingleton_self [I.IsPrime] : I.minimalPrimes =
   constructor
   · exact fun H => (H.2 ⟨inferInstance, rfl.le⟩ H.1.2).antisymm H.1.2
   · rintro (rfl : J = I)
-    refine' ⟨⟨inferInstance, rfl.le⟩, fun _ h _ => h.2⟩
+    exact ⟨⟨inferInstance, rfl.le⟩, fun _ h _ => h.2⟩
 #align ideal.minimal_primes_eq_subsingleton_self Ideal.minimalPrimes_eq_subsingleton_self
 
 end

70fd9563

chore: tidy various files (#10311)

890dba74

Diff

@@ -39,14 +39,14 @@ protected def Ideal.minimalPrimes : Set (Ideal R) :=
   minimals (· ≤ ·) { p | p.IsPrime ∧ I ≤ p }
 #align ideal.minimal_primes Ideal.minimalPrimes
 
+variable (R) in
 /-- `minimalPrimes R` is the set of minimal primes of `R`.
 This is defined as `Ideal.minimalPrimes ⊥`. -/
-def minimalPrimes (R : Type*) [CommSemiring R] : Set (Ideal R) :=
+def minimalPrimes : Set (Ideal R) :=
   Ideal.minimalPrimes ⊥
 #align minimal_primes minimalPrimes
 
-lemma minimalPrimes_eq_minimals {R} [CommSemiring R] :
-    minimalPrimes R = minimals (· ≤ ·) (setOf Ideal.IsPrime) :=
+lemma minimalPrimes_eq_minimals : minimalPrimes R = minimals (· ≤ ·) (setOf Ideal.IsPrime) :=
   congr_arg (minimals (· ≤ ·)) (by simp)
 
 variable {I J}

70fd9563

feat: Lemma on Monoid Localization and Consequences on Minimal Primes (#9640)

Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

ff40d692

Diff

@@ -32,7 +32,7 @@ We provide various results concerning the minimal primes above an ideal
 
 section
 
-variable {R S : Type*} [CommRing R] [CommRing S] (I J : Ideal R)
+variable {R S : Type*} [CommSemiring R] [CommSemiring S] (I J : Ideal R)
 
 /-- `I.minimalPrimes` is the set of ideals that are minimal primes over `I`. -/
 protected def Ideal.minimalPrimes : Set (Ideal R) :=
@@ -41,11 +41,11 @@ protected def Ideal.minimalPrimes : Set (Ideal R) :=
 
 /-- `minimalPrimes R` is the set of minimal primes of `R`.
 This is defined as `Ideal.minimalPrimes ⊥`. -/
-def minimalPrimes (R : Type*) [CommRing R] : Set (Ideal R) :=
+def minimalPrimes (R : Type*) [CommSemiring R] : Set (Ideal R) :=
   Ideal.minimalPrimes ⊥
 #align minimal_primes minimalPrimes
 
-lemma minimalPrimes_eq_minimals {R} [CommRing R] :
+lemma minimalPrimes_eq_minimals {R} [CommSemiring R] :
     minimalPrimes R = minimals (· ≤ ·) (setOf Ideal.IsPrime) :=
   congr_arg (minimals (· ≤ ·)) (by simp)
 
@@ -124,6 +124,12 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective {f : R →+* S}
   apply IsLocalization.map_units _ (show p.primeCompl from ⟨x, h⟩)
 #align ideal.exists_comap_eq_of_mem_minimal_primes_of_injective Ideal.exists_comap_eq_of_mem_minimalPrimes_of_injective
 
+end
+
+section
+
+variable {R S : Type*} [CommRing R] [CommRing S] {I J : Ideal R}
+
 theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S) (p)
     (H : p ∈ (I.comap f).minimalPrimes) : ∃ p' : Ideal S, p'.IsPrime ∧ I ≤ p' ∧ p'.comap f = p := by
   have := H.1.1

70fd9563

feat(AlgebraicGeometry/PrimeSpectrum/*) : the collection of minimal prime ideals of a Noetherian ring is finite (#9088)

Co-PR : #9087 (maximal ideals of Artinian ring are finite)

Co-authored-by: Andrew Yang <the.erd.one@gmail.com> Co-authored-by: Junyan Xu <junyanxumath@gmail.com>

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

f3a26801

Diff

@@ -45,6 +45,10 @@ def minimalPrimes (R : Type*) [CommRing R] : Set (Ideal R) :=
   Ideal.minimalPrimes ⊥
 #align minimal_primes minimalPrimes
 
+lemma minimalPrimes_eq_minimals {R} [CommRing R] :
+    minimalPrimes R = minimals (· ≤ ·) (setOf Ideal.IsPrime) :=
+  congr_arg (minimals (· ≤ ·)) (by simp)
+
 variable {I J}
 
 theorem Ideal.exists_minimalPrimes_le [J.IsPrime] (e : I ≤ J) : ∃ p ∈ I.minimalPrimes, p ≤ J := by

70fd9563

chore: fix typo mimimal to minimal (#7455)

f1a26d74

Diff

@@ -163,7 +163,7 @@ theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)
   exact (H.2 ⟨inferInstance, Ideal.comap_mono hq.1.2⟩ this).antisymm this
 #align ideal.exists_minimal_primes_comap_eq Ideal.exists_minimalPrimes_comap_eq
 
-theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
+theorem Ideal.minimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     {I J : Ideal S} (h : J ∈ I.minimalPrimes) : J.comap f ∈ (I.comap f).minimalPrimes := by
   have := h.1.1
   refine' ⟨⟨inferInstance, Ideal.comap_mono h.1.2⟩, _⟩
@@ -174,7 +174,7 @@ theorem Ideal.mimimal_primes_comap_of_surjective {f : R →+* S} (hf : Function.
   apply h.2 _ _
   · exact ⟨Ideal.map_isPrime_of_surjective hf this, Ideal.le_map_of_comap_le_of_surjective f hf e₁⟩
   · exact Ideal.map_le_of_le_comap e₂
-#align ideal.mimimal_primes_comap_of_surjective Ideal.mimimal_primes_comap_of_surjective
+#align ideal.mimimal_primes_comap_of_surjective Ideal.minimal_primes_comap_of_surjective
 
 theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     (I : Ideal S) : (I.comap f).minimalPrimes = Ideal.comap f '' I.minimalPrimes := by
@@ -184,7 +184,7 @@ theorem Ideal.comap_minimalPrimes_eq_of_surjective {f : R →+* S} (hf : Functio
     obtain ⟨p, h, rfl⟩ := Ideal.exists_minimalPrimes_comap_eq f J H
     exact ⟨p, h, rfl⟩
   · rintro ⟨J, hJ, rfl⟩
-    exact Ideal.mimimal_primes_comap_of_surjective hf hJ
+    exact Ideal.minimal_primes_comap_of_surjective hf hJ
 #align ideal.comap_minimal_primes_eq_of_surjective Ideal.comap_minimalPrimes_eq_of_surjective
 
 theorem Ideal.minimalPrimes_eq_comap :

70fd9563

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

@@ -32,7 +32,7 @@ We provide various results concerning the minimal primes above an ideal
 
 section
 
-variable {R S : Type _} [CommRing R] [CommRing S] (I J : Ideal R)
+variable {R S : Type*} [CommRing R] [CommRing S] (I J : Ideal R)
 
 /-- `I.minimalPrimes` is the set of ideals that are minimal primes over `I`. -/
 protected def Ideal.minimalPrimes : Set (Ideal R) :=
@@ -41,7 +41,7 @@ protected def Ideal.minimalPrimes : Set (Ideal R) :=
 
 /-- `minimalPrimes R` is the set of minimal primes of `R`.
 This is defined as `Ideal.minimalPrimes ⊥`. -/
-def minimalPrimes (R : Type _) [CommRing R] : Set (Ideal R) :=
+def minimalPrimes (R : Type*) [CommRing R] : Set (Ideal R) :=
   Ideal.minimalPrimes ⊥
 #align minimal_primes minimalPrimes

70fd9563

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 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.minimal_prime
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Localization.AtPrime
 import Mathlib.Order.Minimal
 
+#align_import ring_theory.ideal.minimal_prime from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 # Minimal primes

70fd9563

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -77,11 +77,11 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
   congr
   ext p
   refine' ⟨_, _⟩ <;> rintro ⟨⟨a, ha⟩, b⟩
-  . refine' ⟨⟨a, a.radical_le_iff.1 ha⟩, _⟩
-    . simp only [Set.mem_setOf_eq, and_imp] at *
+  · refine' ⟨⟨a, a.radical_le_iff.1 ha⟩, _⟩
+    · simp only [Set.mem_setOf_eq, and_imp] at *
       exact fun _ h2 h3 h4 => b h2 (h2.radical_le_iff.2 h3) h4
-  . refine' ⟨⟨a, a.radical_le_iff.2 ha⟩, _⟩
-    . simp only [Set.mem_setOf_eq, and_imp] at *
+  · refine' ⟨⟨a, a.radical_le_iff.2 ha⟩, _⟩
+    · simp only [Set.mem_setOf_eq, and_imp] at *
       exact fun _ h2 h3 h4 => b h2 (h2.radical_le_iff.1 h3) h4
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
 
@@ -138,7 +138,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       (RingHom.kerLift_injective f') (p.map <| Ideal.Quotient.mk <| RingHom.ker f') this
     refine' ⟨p'.comap <| Ideal.Quotient.mk I, Ideal.IsPrime.comap _, _, _⟩
     · exact Ideal.mk_ker.symm.trans_le (Ideal.comap_mono bot_le)
-    . convert congr_arg (Ideal.comap <| Ideal.Quotient.mk <| RingHom.ker f') hp₂
+    · convert congr_arg (Ideal.comap <| Ideal.Quotient.mk <| RingHom.ker f') hp₂
       rwa [Ideal.comap_map_of_surjective (Ideal.Quotient.mk <| RingHom.ker f')
         Ideal.Quotient.mk_surjective, eq_comm, sup_eq_left]
   refine' ⟨⟨_, bot_le⟩, _⟩
@@ -199,8 +199,7 @@ theorem Ideal.minimalPrimes_eq_comap :
 theorem Ideal.minimalPrimes_eq_subsingleton (hI : I.IsPrimary) : I.minimalPrimes = {I.radical} := by
   ext J
   constructor
-  ·
-    exact fun H =>
+  · exact fun H =>
       let e := H.1.1.radical_le_iff.mpr H.1.2
       (H.2 ⟨Ideal.isPrime_radical hI, Ideal.le_radical⟩ e).antisymm e
   · rintro (rfl : J = I.radical)

70fd9563

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

@@ -90,7 +90,7 @@ theorem Ideal.sInf_minimalPrimes : sInf I.minimalPrimes = I.radical := by
   rw [I.radical_eq_sInf]
   apply le_antisymm
   · intro x hx
-    rw [Ideal.mem_sInf] at hx⊢
+    rw [Ideal.mem_sInf] at hx ⊢
     rintro J ⟨e, hJ⟩
     obtain ⟨p, hp, hp'⟩ := Ideal.exists_minimalPrimes_le e
     exact hp' (hx hp)

70fd9563

chore: add space after exacts (#4945)

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

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

bf799bb9

Diff

@@ -153,7 +153,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
     · refine' ⟨inferInstance, (Ideal.mk_ker.trans e).symm.trans_le (Ideal.comap_mono bot_le)⟩
     · refine' (Ideal.comap_mono hq').trans _
       rw [Ideal.comap_map_of_surjective]
-      exacts[sup_le rfl.le this, Ideal.Quotient.mk_surjective]
+      exacts [sup_le rfl.le this, Ideal.Quotient.mk_surjective]
 #align ideal.exists_comap_eq_of_mem_minimal_primes Ideal.exists_comap_eq_of_mem_minimalPrimes
 
 theorem Ideal.exists_minimalPrimes_comap_eq {I : Ideal S} (f : R →+* S) (p)

70fd9563

feat: port RingTheory.Ideal.MinimalPrime (#4146)

Please feel free to push changes to this branch.

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

67e16b06

`ring_theory.ideal.minimal_prime` ⟷ `Mathlib.RingTheory.Ideal.MinimalPrime`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 547

ring_theory.ideal.minimal_prime ⟷ Mathlib.RingTheory.Ideal.MinimalPrime

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 547

`ring_theory.ideal.minimal_prime` ⟷ `Mathlib.RingTheory.Ideal.MinimalPrime`