ring_theory.jacobson_ideal ⟷ Mathlib.RingTheory.JacobsonIdeal

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

@@ -124,7 +124,7 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
         let ⟨p, hpi, q, hq, hpq⟩ := Submodule.mem_sup.1 ((eq_top_iff_one _).1 hxy)
         let ⟨r, hr⟩ := mem_span_singleton'.1 hq
         ⟨r, by
-          rw [mul_assoc, ← mul_add_one, hr, ← hpq, ← neg_sub, add_sub_cancel] <;>
+          rw [mul_assoc, ← mul_add_one, hr, ← hpq, ← neg_sub, add_sub_cancel_right] <;>
             exact I.neg_mem hpi⟩)
       fun hxy : I ⊔ span {y * x + 1} ≠ ⊤ =>
       let ⟨M, hm1, hm2⟩ := exists_le_maximal _ hxy
@@ -132,7 +132,7 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
       fun hxm =>
       hm1.1.1 <|
         (eq_top_iff_one _).2 <|
-          add_sub_cancel' (y * x) 1 ▸
+          add_sub_cancel_left (y * x) 1 ▸
             M.sub_mem (le_sup_right.trans hm2 <| subset_span rfl) (M.mul_mem_left _ hxm),
     fun hx =>
     mem_sInf.2 fun M ⟨him, hm⟩ =>
@@ -196,7 +196,7 @@ theorem eq_jacobson_iff_sInf_maximal' :
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ∉ » I) -/
 #print Ideal.eq_jacobson_iff_not_mem /-
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
@@ -459,7 +459,8 @@ theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R
     (fun h : I ⊔ span {x} = ⊤ =>
       let ⟨p, hpi, q, hq, hpq⟩ := Submodule.mem_sup.1 ((eq_top_iff_one _).1 h)
       let ⟨r, hr⟩ := mem_span_singleton.1 hq
-      Or.inr ⟨r, by rw [← hpq, mul_comm, ← hr, ← neg_sub, add_sub_cancel] <;> exact I.neg_mem hpi⟩)
+      Or.inr
+        ⟨r, by rw [← hpq, mul_comm, ← hr, ← neg_sub, add_sub_cancel_right] <;> exact I.neg_mem hpi⟩)
     fun h : I ⊔ span {x} ≠ ⊤ =>
     Or.inl <|
       le_trans le_sup_right (hi.le_jacobson le_sup_left h) <| mem_span_singleton.2 <| dvd_refl x

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

@@ -205,8 +205,8 @@ theorem eq_jacobson_iff_not_mem :
   by
   constructor
   · intro h x hx
-    erw [← h, mem_Inf] at hx 
-    push_neg at hx 
+    erw [← h, mem_Inf] at hx
+    push_neg at hx
     exact hx
   · refine' fun h => le_antisymm (fun x hx => _) le_jacobson
     contrapose hx
@@ -310,7 +310,7 @@ theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
 theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥ : Ideal R)) :
     IsUnit r := by
   cases' exists_mul_sub_mem_of_sub_one_mem_jacobson r h with s hs
-  rw [mem_bot, sub_eq_zero, mul_comm] at hs 
+  rw [mem_bot, sub_eq_zero, mul_comm] at hs
   exact isUnit_of_mul_eq_one _ _ hs
 #align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_bot
 -/
@@ -338,11 +338,11 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
   constructor
   · intro h
     replace h := congr_arg (map (Quotient.mk' I)) h
-    rw [map_jacobson_of_surjective hf (le_of_eq mk_ker)] at h 
+    rw [map_jacobson_of_surjective hf (le_of_eq mk_ker)] at h
     simpa using h
   · intro h
     replace h := congr_arg (comap (Quotient.mk' I)) h
-    rw [comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at h 
+    rw [comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at h
     simpa using h
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
 -/
@@ -358,11 +358,11 @@ theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
   · intro h
     have := congr_arg (map (Quotient.mk' I)) h
     rw [map_radical_of_surjective hf (le_of_eq mk_ker),
-      map_jacobson_of_surjective hf (le_of_eq mk_ker)] at this 
+      map_jacobson_of_surjective hf (le_of_eq mk_ker)] at this
     simpa using this
   · intro h
     have := congr_arg (comap (Quotient.mk' I)) h
-    rw [comap_radical, comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at this 
+    rw [comap_radical, comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at this
     simpa using this
 #align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot
 -/
@@ -397,7 +397,7 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     by
     rw [← hj.2, jacobson_eq_iff_jacobson_quotient_eq_bot]
     replace this := congr_arg (map (polynomial_quotient_equiv_quotient_polynomial j).toRingHom) this
-    rwa [map_jacobson_of_bijective _, map_bot] at this 
+    rwa [map_jacobson_of_bijective _, map_bot] at this
     exact RingEquiv.bijective (polynomial_quotient_equiv_quotient_polynomial j)
   refine' eq_bot_iff.2 fun f hf => _
   simpa [(fun hX => by simpa using congr_arg (fun f => coeff f 1) hX : (X : (R ⧸ j)[X]) ≠ 0)] using
@@ -411,7 +411,7 @@ theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) =
   by
   refine' eq_bot_iff.2 (le_trans jacobson_bot_polynomial_le_Inf_map_maximal _)
   refine' fun f hf => (Submodule.mem_bot _).2 (Polynomial.ext fun n => trans _ (coeff_zero n).symm)
-  suffices f.coeff n ∈ Ideal.jacobson ⊥ by rwa [h, Submodule.mem_bot] at this 
+  suffices f.coeff n ∈ Ideal.jacobson ⊥ by rwa [h, Submodule.mem_bot] at this
   exact mem_Inf.2 fun j hj => (mem_map_C_iff.1 ((mem_Inf.1 hf) ⟨j, ⟨hj.2, rfl⟩⟩)) n
 #align ideal.jacobson_bot_polynomial_of_jacobson_bot Ideal.jacobson_bot_polynomial_of_jacobson_bot
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
 -/
-import Mathbin.RingTheory.Ideal.Quotient
-import Mathbin.RingTheory.Polynomial.Quotient
+import RingTheory.Ideal.Quotient
+import RingTheory.Polynomial.Quotient
 
 #align_import ring_theory.jacobson_ideal from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 
@@ -196,7 +196,7 @@ theorem eq_jacobson_iff_sInf_maximal' :
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » I) -/
 #print Ideal.eq_jacobson_iff_not_mem /-
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.jacobson_ideal
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Ideal.Quotient
 import Mathbin.RingTheory.Polynomial.Quotient
 
+#align_import ring_theory.jacobson_ideal from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Jacobson radical
 
@@ -199,7 +196,7 @@ theorem eq_jacobson_iff_sInf_maximal' :
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
 #print Ideal.eq_jacobson_iff_not_mem /-
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/

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

@@ -68,8 +68,10 @@ def jacobson (I : Ideal R) : Ideal R :=
 #align ideal.jacobson Ideal.jacobson
 -/
 
+#print Ideal.le_jacobson /-
 theorem le_jacobson : I ≤ jacobson I := fun x hx => mem_sInf.mpr fun J hJ => hJ.left hx
 #align ideal.le_jacobson Ideal.le_jacobson
+-/
 
 #print Ideal.jacobson_idem /-
 @[simp]
@@ -78,11 +80,14 @@ theorem jacobson_idem : jacobson (jacobson I) = jacobson I :=
 #align ideal.jacobson_idem Ideal.jacobson_idem
 -/
 
+#print Ideal.jacobson_top /-
 @[simp]
 theorem jacobson_top : jacobson (⊤ : Ideal R) = ⊤ :=
   eq_top_iff.2 le_jacobson
 #align ideal.jacobson_top Ideal.jacobson_top
+-/
 
+#print Ideal.jacobson_eq_top_iff /-
 @[simp]
 theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
   ⟨fun H =>
@@ -94,9 +99,12 @@ theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
         H,
     fun H => eq_top_iff.2 <| le_sInf fun J ⟨hij, hj⟩ => H ▸ hij⟩
 #align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iff
+-/
 
+#print Ideal.jacobson_eq_bot /-
 theorem jacobson_eq_bot : jacobson I = ⊥ → I = ⊥ := fun h => eq_bot_iff.mpr (h ▸ le_jacobson)
 #align ideal.jacobson_eq_bot Ideal.jacobson_eq_bot
+-/
 
 #print Ideal.jacobson_eq_self_of_isMaximal /-
 theorem jacobson_eq_self_of_isMaximal [H : IsMaximal I] : I.jacobson = I :=
@@ -111,6 +119,7 @@ instance (priority := 100) jacobson.isMaximal [H : IsMaximal I] : IsMaximal (jac
 #align ideal.jacobson.is_maximal Ideal.jacobson.isMaximal
 -/
 
+#print Ideal.mem_jacobson_iff /-
 theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x + z - 1 ∈ I :=
   ⟨fun hx y =>
     by_cases
@@ -143,14 +152,18 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
                   exact M.mul_mem_left _ hi)
                 (him hz)⟩
 #align ideal.mem_jacobson_iff Ideal.mem_jacobson_iff
+-/
 
+#print Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson /-
 theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r - 1 ∈ jacobson I) :
     ∃ s, s * r - 1 ∈ I := by
   cases' mem_jacobson_iff.1 h 1 with s hs
   use s
   simpa [mul_sub] using hs
 #align ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson
+-/
 
+#print Ideal.eq_jacobson_iff_sInf_maximal /-
 /-- An ideal equals its Jacobson radical iff it is the intersection of a set of maximal ideals.
 Allowing the set to include ⊤ is equivalent, and is included only to simplify some proofs. -/
 theorem eq_jacobson_iff_sInf_maximal :
@@ -165,7 +178,9 @@ theorem eq_jacobson_iff_sInf_maximal :
   · exact (mem_Inf.1 hx) ⟨le_sInf_iff.1 (le_of_eq hInf) I hI, IsMax⟩
   · exact is_top.symm ▸ Submodule.mem_top
 #align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximal
+-/
 
+#print Ideal.eq_jacobson_iff_sInf_maximal' /-
 theorem eq_jacobson_iff_sInf_maximal' :
     I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, ∀ (K : Ideal R), J < K → K = ⊤) ∧ I = sInf M :=
   eq_jacobson_iff_sInf_maximal.trans
@@ -182,8 +197,10 @@ theorem eq_jacobson_iff_sInf_maximal' :
           Or.rec_on (Classical.em (J = ⊤)) (fun h => Or.inr h) fun h => Or.inl ⟨⟨h, hM.1 J hJ⟩⟩,
           hM.2⟩⟩⟩
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » I) -/
+#print Ideal.eq_jacobson_iff_not_mem /-
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
 theorem eq_jacobson_iff_not_mem :
@@ -200,7 +217,9 @@ theorem eq_jacobson_iff_not_mem :
     push_neg
     exact h x hx
 #align ideal.eq_jacobson_iff_not_mem Ideal.eq_jacobson_iff_not_mem
+-/
 
+#print Ideal.map_jacobson_of_surjective /-
 theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) :
     RingHom.ker f ≤ I → map f I.jacobson = (map f I).jacobson :=
   by
@@ -219,18 +238,24 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     · exact htop.symm ▸ Set.mem_insert ⊤ _
     · exact Set.mem_insert_of_mem ⊤ ⟨map_mono hJ.1.1, hmax⟩
 #align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjective
+-/
 
+#print Ideal.map_jacobson_of_bijective /-
 theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
     map f I.jacobson = (map f I).jacobson :=
   map_jacobson_of_surjective hf.right
     (le_trans (le_of_eq (f.injective_iff_ker_eq_bot.1 hf.left)) bot_le)
 #align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijective
+-/
 
+#print Ideal.comap_jacobson /-
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
     comap f K.jacobson = sInf (comap f '' {J : Ideal S | K ≤ J ∧ J.IsMaximal}) :=
   trans (comap_sInf' f _) sInf_eq_iInf.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
+-/
 
+#print Ideal.comap_jacobson_of_surjective /-
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :
     comap f K.jacobson = (comap f K).jacobson :=
   by
@@ -254,7 +279,9 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
     haveI : J.is_maximal := hJ.right
     refine' sInf_le ⟨comap_mono hJ.left, comap_is_maximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective
+-/
 
+#print Ideal.jacobson_mono /-
 @[mono]
 theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson :=
   by
@@ -262,6 +289,7 @@ theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson :=
   erw [mem_Inf] at hx ⊢
   exact fun K ⟨hK, hK_max⟩ => hx ⟨trans h hK, hK_max⟩
 #align ideal.jacobson_mono Ideal.jacobson_mono
+-/
 
 end Ring
 
@@ -269,9 +297,11 @@ section CommRing
 
 variable [CommRing R] [CommRing S] {I : Ideal R}
 
+#print Ideal.radical_le_jacobson /-
 theorem radical_le_jacobson : radical I ≤ jacobson I :=
   le_sInf fun J hJ => (radical_eq_sInf I).symm ▸ sInf_le ⟨hJ.left, IsMaximal.isPrime hJ.right⟩
 #align ideal.radical_le_jacobson Ideal.radical_le_jacobson
+-/
 
 #print Ideal.isRadical_of_eq_jacobson /-
 theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
@@ -279,13 +309,16 @@ theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
 #align ideal.is_radical_of_eq_jacobson Ideal.isRadical_of_eq_jacobson
 -/
 
+#print Ideal.isUnit_of_sub_one_mem_jacobson_bot /-
 theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥ : Ideal R)) :
     IsUnit r := by
   cases' exists_mul_sub_mem_of_sub_one_mem_jacobson r h with s hs
   rw [mem_bot, sub_eq_zero, mul_comm] at hs 
   exact isUnit_of_mul_eq_one _ _ hs
 #align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_bot
+-/
 
+#print Ideal.mem_jacobson_bot /-
 theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsUnit (x * y + 1) :=
   ⟨fun hx y =>
     let ⟨z, hz⟩ := (mem_jacobson_iff.1 hx) y
@@ -296,7 +329,9 @@ theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsU
       let ⟨b, hb⟩ := isUnit_iff_exists_inv.1 (h y)
       ⟨b, (Submodule.mem_bot R).2 (hb ▸ by ring)⟩⟩
 #align ideal.mem_jacobson_bot Ideal.mem_jacobson_bot
+-/
 
+#print Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot /-
 /-- An ideal `I` of `R` is equal to its Jacobson radical if and only if
 the Jacobson radical of the quotient ring `R/I` is the zero ideal -/
 theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
@@ -313,7 +348,9 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
     rw [comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at h 
     simpa using h
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
+-/
 
+#print Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot /-
 /-- The standard radical and Jacobson radical of an ideal `I` of `R` are equal if and only if
 the nilradical and Jacobson radical of the quotient ring `R/I` coincide -/
 theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
@@ -331,6 +368,7 @@ theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
     rw [comap_radical, comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at this 
     simpa using this
 #align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot
+-/
 
 #print Ideal.jacobson_radical_eq_jacobson /-
 theorem jacobson_radical_eq_jacobson : I.radical.jacobson = I.jacobson :=
@@ -351,6 +389,7 @@ open Polynomial
 
 variable [CommRing R]
 
+#print Ideal.jacobson_bot_polynomial_le_sInf_map_maximal /-
 theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' {J : Ideal R | J.IsMaximal}) :=
   by
@@ -367,7 +406,9 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
   simpa [(fun hX => by simpa using congr_arg (fun f => coeff f 1) hX : (X : (R ⧸ j)[X]) ≠ 0)] using
     eq_C_of_degree_eq_zero (degree_eq_zero_of_is_unit ((mem_jacobson_bot.1 hf) X))
 #align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximal
+-/
 
+#print Ideal.jacobson_bot_polynomial_of_jacobson_bot /-
 theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) = ⊥) :
     jacobson (⊥ : Ideal R[X]) = ⊥ :=
   by
@@ -376,6 +417,7 @@ theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) =
   suffices f.coeff n ∈ Ideal.jacobson ⊥ by rwa [h, Submodule.mem_bot] at this 
   exact mem_Inf.2 fun j hj => (mem_map_C_iff.1 ((mem_Inf.1 hf) ⟨j, ⟨hj.2, rfl⟩⟩)) n
 #align ideal.jacobson_bot_polynomial_of_jacobson_bot Ideal.jacobson_bot_polynomial_of_jacobson_bot
+-/
 
 end Polynomial
 
@@ -405,12 +447,15 @@ theorem isLocal_of_isMaximal_radical {I : Ideal R} (hi : IsMaximal (radical I))
 #align ideal.is_local_of_is_maximal_radical Ideal.isLocal_of_isMaximal_radical
 -/
 
+#print Ideal.IsLocal.le_jacobson /-
 theorem IsLocal.le_jacobson {I J : Ideal R} (hi : IsLocal I) (hij : I ≤ J) (hj : J ≠ ⊤) :
     J ≤ jacobson I :=
   let ⟨M, hm, hjm⟩ := exists_le_maximal J hj
   le_trans hjm <| le_of_eq <| Eq.symm <| hi.1.eq_of_le hm.1.1 <| sInf_le ⟨le_trans hij hjm, hm⟩
 #align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobson
+-/
 
+#print Ideal.IsLocal.mem_jacobson_or_exists_inv /-
 theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R) :
     x ∈ jacobson I ∨ ∃ y, y * x - 1 ∈ I :=
   by_cases
@@ -422,6 +467,7 @@ theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R
     Or.inl <|
       le_trans le_sup_right (hi.le_jacobson le_sup_left h) <| mem_span_singleton.2 <| dvd_refl x
 #align ideal.is_local.mem_jacobson_or_exists_inv Ideal.IsLocal.mem_jacobson_or_exists_inv
+-/
 
 end IsLocal
 

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

@@ -183,7 +183,7 @@ theorem eq_jacobson_iff_sInf_maximal' :
           hM.2⟩⟩⟩
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » I) -/
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
 theorem eq_jacobson_iff_not_mem :

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

@@ -64,7 +64,7 @@ variable [Ring R] [Ring S] {I : Ideal R}
 #print Ideal.jacobson /-
 /-- The Jacobson radical of `I` is the infimum of all maximal (left) ideals containing `I`. -/
 def jacobson (I : Ideal R) : Ideal R :=
-  sInf { J : Ideal R | I ≤ J ∧ IsMaximal J }
+  sInf {J : Ideal R | I ≤ J ∧ IsMaximal J}
 #align ideal.jacobson Ideal.jacobson
 -/
 
@@ -156,7 +156,7 @@ Allowing the set to include ⊤ is equivalent, and is included only to simplify
 theorem eq_jacobson_iff_sInf_maximal :
     I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, IsMaximal J ∨ J = ⊤) ∧ I = sInf M :=
   by
-  use fun hI => ⟨{ J : Ideal R | I ≤ J ∧ J.IsMaximal }, ⟨fun _ hJ => Or.inl hJ.right, hI.symm⟩⟩
+  use fun hI => ⟨{J : Ideal R | I ≤ J ∧ J.IsMaximal}, ⟨fun _ hJ => Or.inl hJ.right, hI.symm⟩⟩
   rintro ⟨M, hM, hInf⟩
   refine' le_antisymm (fun x hx => _) le_jacobson
   rw [hInf, mem_Inf]
@@ -192,7 +192,7 @@ theorem eq_jacobson_iff_not_mem :
   constructor
   · intro h x hx
     erw [← h, mem_Inf] at hx 
-    push_neg  at hx 
+    push_neg at hx 
     exact hx
   · refine' fun h => le_antisymm (fun x hx => _) le_jacobson
     contrapose hx
@@ -206,7 +206,7 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
   by
   intro h
   unfold Ideal.jacobson
-  have : ∀ J ∈ { J : Ideal R | I ≤ J ∧ J.IsMaximal }, f.ker ≤ J := fun J hJ => le_trans h hJ.left
+  have : ∀ J ∈ {J : Ideal R | I ≤ J ∧ J.IsMaximal}, f.ker ≤ J := fun J hJ => le_trans h hJ.left
   refine' trans (map_Inf hf this) (le_antisymm _ _)
   · refine'
       sInf_le_sInf fun J hJ =>
@@ -227,7 +227,7 @@ theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
 #align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijective
 
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
-    comap f K.jacobson = sInf (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
+    comap f K.jacobson = sInf (comap f '' {J : Ideal S | K ≤ J ∧ J.IsMaximal}) :=
   trans (comap_sInf' f _) sInf_eq_iInf.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
 
@@ -352,7 +352,7 @@ open Polynomial
 variable [CommRing R]
 
 theorem jacobson_bot_polynomial_le_sInf_map_maximal :
-    jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
+    jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' {J : Ideal R | J.IsMaximal}) :=
   by
   refine' le_sInf fun J => exists_imp.2 fun j hj => _
   haveI : j.is_maximal := hj.1

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

@@ -191,8 +191,8 @@ theorem eq_jacobson_iff_not_mem :
   by
   constructor
   · intro h x hx
-    erw [← h, mem_Inf] at hx
-    push_neg  at hx
+    erw [← h, mem_Inf] at hx 
+    push_neg  at hx 
     exact hx
   · refine' fun h => le_antisymm (fun x hx => _) le_jacobson
     contrapose hx
@@ -259,7 +259,7 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
 theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson :=
   by
   intro h x hx
-  erw [mem_Inf] at hx⊢
+  erw [mem_Inf] at hx ⊢
   exact fun K ⟨hK, hK_max⟩ => hx ⟨trans h hK, hK_max⟩
 #align ideal.jacobson_mono Ideal.jacobson_mono
 
@@ -282,7 +282,7 @@ theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
 theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥ : Ideal R)) :
     IsUnit r := by
   cases' exists_mul_sub_mem_of_sub_one_mem_jacobson r h with s hs
-  rw [mem_bot, sub_eq_zero, mul_comm] at hs
+  rw [mem_bot, sub_eq_zero, mul_comm] at hs 
   exact isUnit_of_mul_eq_one _ _ hs
 #align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_bot
 
@@ -306,11 +306,11 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
   constructor
   · intro h
     replace h := congr_arg (map (Quotient.mk' I)) h
-    rw [map_jacobson_of_surjective hf (le_of_eq mk_ker)] at h
+    rw [map_jacobson_of_surjective hf (le_of_eq mk_ker)] at h 
     simpa using h
   · intro h
     replace h := congr_arg (comap (Quotient.mk' I)) h
-    rw [comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at h
+    rw [comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at h 
     simpa using h
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
 
@@ -324,11 +324,11 @@ theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
   · intro h
     have := congr_arg (map (Quotient.mk' I)) h
     rw [map_radical_of_surjective hf (le_of_eq mk_ker),
-      map_jacobson_of_surjective hf (le_of_eq mk_ker)] at this
+      map_jacobson_of_surjective hf (le_of_eq mk_ker)] at this 
     simpa using this
   · intro h
     have := congr_arg (comap (Quotient.mk' I)) h
-    rw [comap_radical, comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at this
+    rw [comap_radical, comap_jacobson_of_surjective hf, ← (Quotient.mk' I).ker_eq_comap_bot] at this 
     simpa using this
 #align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot
 
@@ -361,7 +361,7 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     by
     rw [← hj.2, jacobson_eq_iff_jacobson_quotient_eq_bot]
     replace this := congr_arg (map (polynomial_quotient_equiv_quotient_polynomial j).toRingHom) this
-    rwa [map_jacobson_of_bijective _, map_bot] at this
+    rwa [map_jacobson_of_bijective _, map_bot] at this 
     exact RingEquiv.bijective (polynomial_quotient_equiv_quotient_polynomial j)
   refine' eq_bot_iff.2 fun f hf => _
   simpa [(fun hX => by simpa using congr_arg (fun f => coeff f 1) hX : (X : (R ⧸ j)[X]) ≠ 0)] using
@@ -373,7 +373,7 @@ theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) =
   by
   refine' eq_bot_iff.2 (le_trans jacobson_bot_polynomial_le_Inf_map_maximal _)
   refine' fun f hf => (Submodule.mem_bot _).2 (Polynomial.ext fun n => trans _ (coeff_zero n).symm)
-  suffices f.coeff n ∈ Ideal.jacobson ⊥ by rwa [h, Submodule.mem_bot] at this
+  suffices f.coeff n ∈ Ideal.jacobson ⊥ by rwa [h, Submodule.mem_bot] at this 
   exact mem_Inf.2 fun j hj => (mem_map_C_iff.1 ((mem_Inf.1 hf) ⟨j, ⟨hj.2, rfl⟩⟩)) n
 #align ideal.jacobson_bot_polynomial_of_jacobson_bot Ideal.jacobson_bot_polynomial_of_jacobson_bot
 

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

@@ -53,7 +53,7 @@ namespace Ideal
 
 variable {R : Type u} {S : Type v}
 
-open Polynomial
+open scoped Polynomial
 
 section Jacobson
 

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

@@ -68,12 +68,6 @@ def jacobson (I : Ideal R) : Ideal R :=
 #align ideal.jacobson Ideal.jacobson
 -/
 
-/- warning: ideal.le_jacobson -> Ideal.le_jacobson is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I (Ideal.jacobson.{u1} R _inst_1 I)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I (Ideal.jacobson.{u1} R _inst_1 I)
-Case conversion may be inaccurate. Consider using '#align ideal.le_jacobson Ideal.le_jacobsonₓ'. -/
 theorem le_jacobson : I ≤ jacobson I := fun x hx => mem_sInf.mpr fun J hJ => hJ.left hx
 #align ideal.le_jacobson Ideal.le_jacobson
 
@@ -84,23 +78,11 @@ theorem jacobson_idem : jacobson (jacobson I) = jacobson I :=
 #align ideal.jacobson_idem Ideal.jacobson_idem
 -/
 
-/- warning: ideal.jacobson_top -> Ideal.jacobson_top is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_top Ideal.jacobson_topₓ'. -/
 @[simp]
 theorem jacobson_top : jacobson (⊤ : Ideal R) = ⊤ :=
   eq_top_iff.2 le_jacobson
 #align ideal.jacobson_top Ideal.jacobson_top
 
-/- warning: ideal.jacobson_eq_top_iff -> Ideal.jacobson_eq_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iffₓ'. -/
 @[simp]
 theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
   ⟨fun H =>
@@ -113,12 +95,6 @@ theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
     fun H => eq_top_iff.2 <| le_sInf fun J ⟨hij, hj⟩ => H ▸ hij⟩
 #align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iff
 
-/- warning: ideal.jacobson_eq_bot -> Ideal.jacobson_eq_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_bot Ideal.jacobson_eq_botₓ'. -/
 theorem jacobson_eq_bot : jacobson I = ⊥ → I = ⊥ := fun h => eq_bot_iff.mpr (h ▸ le_jacobson)
 #align ideal.jacobson_eq_bot Ideal.jacobson_eq_bot
 
@@ -135,12 +111,6 @@ instance (priority := 100) jacobson.isMaximal [H : IsMaximal I] : IsMaximal (jac
 #align ideal.jacobson.is_maximal Ideal.jacobson.isMaximal
 -/
 
-/- warning: ideal.mem_jacobson_iff -> Ideal.mem_jacobson_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {x : R}, Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Ideal.jacobson.{u1} R _inst_1 I)) (forall (y : R), Exists.{succ u1} R (fun (z : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) z y) x) z) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) I))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {x : R}, Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Ideal.jacobson.{u1} R _inst_1 I)) (forall (y : R), Exists.{succ u1} R (fun (z : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) z y) x) z) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) I))
-Case conversion may be inaccurate. Consider using '#align ideal.mem_jacobson_iff Ideal.mem_jacobson_iffₓ'. -/
 theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x + z - 1 ∈ I :=
   ⟨fun hx y =>
     by_cases
@@ -174,12 +144,6 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
                 (him hz)⟩
 #align ideal.mem_jacobson_iff Ideal.mem_jacobson_iff
 
-/- warning: ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson -> Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} (r : R), (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) r (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (Ideal.jacobson.{u1} R _inst_1 I)) -> (Exists.{succ u1} R (fun (s : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) s r) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) I))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} (r : R), (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) r (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Ideal.jacobson.{u1} R _inst_1 I)) -> (Exists.{succ u1} R (fun (s : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) s r) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) I))
-Case conversion may be inaccurate. Consider using '#align ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobsonₓ'. -/
 theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r - 1 ∈ jacobson I) :
     ∃ s, s * r - 1 ∈ I := by
   cases' mem_jacobson_iff.1 h 1 with s hs
@@ -187,12 +151,6 @@ theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r
   simpa [mul_sub] using hs
 #align ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson
 
-/- warning: ideal.eq_jacobson_iff_Inf_maximal -> Ideal.eq_jacobson_iff_sInf_maximal is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (Or (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) J) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (Or (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) J) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
-Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximalₓ'. -/
 /-- An ideal equals its Jacobson radical iff it is the intersection of a set of maximal ideals.
 Allowing the set to include ⊤ is equivalent, and is included only to simplify some proofs. -/
 theorem eq_jacobson_iff_sInf_maximal :
@@ -208,12 +166,6 @@ theorem eq_jacobson_iff_sInf_maximal :
   · exact is_top.symm ▸ Submodule.mem_top
 #align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximal
 
-/- warning: ideal.eq_jacobson_iff_Inf_maximal' -> Ideal.eq_jacobson_iff_sInf_maximal' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (forall (K : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) J K) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) K (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (forall (K : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLT.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) J K) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) K (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
-Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'ₓ'. -/
 theorem eq_jacobson_iff_sInf_maximal' :
     I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, ∀ (K : Ideal R), J < K → K = ⊤) ∧ I = sInf M :=
   eq_jacobson_iff_sInf_maximal.trans
@@ -231,12 +183,6 @@ theorem eq_jacobson_iff_sInf_maximal' :
           hM.2⟩⟩⟩
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 
-/- warning: ideal.eq_jacobson_iff_not_mem -> Ideal.eq_jacobson_iff_not_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (forall (x : R), (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x I)) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (fun (M : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) => And (And (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I M) (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) M)) (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x M)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (forall (x : R), (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x I)) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (fun (M : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) => And (And (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I M) (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) M)) (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x M)))))
-Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_not_mem Ideal.eq_jacobson_iff_not_memₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
@@ -255,12 +201,6 @@ theorem eq_jacobson_iff_not_mem :
     exact h x hx
 #align ideal.eq_jacobson_iff_not_mem Ideal.eq_jacobson_iff_not_mem
 
-/- warning: ideal.map_jacobson_of_surjective -> Ideal.map_jacobson_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
-Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjectiveₓ'. -/
 theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) :
     RingHom.ker f ≤ I → map f I.jacobson = (map f I).jacobson :=
   by
@@ -280,35 +220,17 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     · exact Set.mem_insert_of_mem ⊤ ⟨map_mono hJ.1.1, hmax⟩
 #align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjective
 
-/- warning: ideal.map_jacobson_of_bijective -> Ideal.map_jacobson_of_bijective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))}, (Function.Bijective.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Bijective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
-Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijectiveₓ'. -/
 theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
     map f I.jacobson = (map f I).jacobson :=
   map_jacobson_of_surjective hf.right
     (le_trans (le_of_eq (f.injective_iff_ker_eq_bot.1 hf.left)) bot_le)
 #align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijective
 
-/- warning: ideal.comap_jacobson -> Ideal.comap_jacobson is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))} {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.image.{u2, u1} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f) (setOf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (fun (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) => And (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (SetLike.partialOrder.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) K J) (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S _inst_2) J)))))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))} {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.image.{u2, u1} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) (setOf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (fun (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) => And (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Preorder.toLE.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))) K J) (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S _inst_2) J)))))
-Case conversion may be inaccurate. Consider using '#align ideal.comap_jacobson Ideal.comap_jacobsonₓ'. -/
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
     comap f K.jacobson = sInf (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
   trans (comap_sInf' f _) sInf_eq_iInf.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
 
-/- warning: ideal.comap_jacobson_of_surjective -> Ideal.comap_jacobson_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f K)))
-but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f K)))
-Case conversion may be inaccurate. Consider using '#align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjectiveₓ'. -/
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :
     comap f K.jacobson = (comap f K).jacobson :=
   by
@@ -333,12 +255,6 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
     refine' sInf_le ⟨comap_mono hJ.left, comap_is_maximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective
 
-/- warning: ideal.jacobson_mono -> Ideal.jacobson_mono is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I J) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ideal.jacobson.{u1} R _inst_1 I) (Ideal.jacobson.{u1} R _inst_1 J))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I J) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Ideal.jacobson.{u1} R _inst_1 I) (Ideal.jacobson.{u1} R _inst_1 J))
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_mono Ideal.jacobson_monoₓ'. -/
 @[mono]
 theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson :=
   by
@@ -353,12 +269,6 @@ section CommRing
 
 variable [CommRing R] [CommRing S] {I : Ideal R}
 
-/- warning: ideal.radical_le_jacobson -> Ideal.radical_le_jacobson 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))}, LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{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))}, 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)))))))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)
-Case conversion may be inaccurate. Consider using '#align ideal.radical_le_jacobson Ideal.radical_le_jacobsonₓ'. -/
 theorem radical_le_jacobson : radical I ≤ jacobson I :=
   le_sInf fun J hJ => (radical_eq_sInf I).symm ▸ sInf_le ⟨hJ.left, IsMaximal.isPrime hJ.right⟩
 #align ideal.radical_le_jacobson Ideal.radical_le_jacobson
@@ -369,12 +279,6 @@ theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
 #align ideal.is_radical_of_eq_jacobson Ideal.isRadical_of_eq_jacobson
 -/
 
-/- warning: ideal.is_unit_of_sub_one_mem_jacobson_bot -> Ideal.isUnit_of_sub_one_mem_jacobson_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (r : R), (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) r (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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))))))) -> (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) r)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (r : R), (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) r (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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))))))) -> (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) r)
-Case conversion may be inaccurate. Consider using '#align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_botₓ'. -/
 theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥ : Ideal R)) :
     IsUnit r := by
   cases' exists_mul_sub_mem_of_sub_one_mem_jacobson r h with s hs
@@ -382,12 +286,6 @@ theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥
   exact isUnit_of_mul_eq_one _ _ hs
 #align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_bot
 
-/- warning: ideal.mem_jacobson_bot -> Ideal.mem_jacobson_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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))))))) (forall (y : R), IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x y) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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))))))) (forall (y : R), IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x y) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align ideal.mem_jacobson_bot Ideal.mem_jacobson_botₓ'. -/
 theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsUnit (x * y + 1) :=
   ⟨fun hx y =>
     let ⟨z, hz⟩ := (mem_jacobson_iff.1 hx) y
@@ -399,9 +297,6 @@ theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsU
       ⟨b, (Submodule.mem_bot R).2 (hb ▸ by ring)⟩⟩
 #align ideal.mem_jacobson_bot Ideal.mem_jacobson_bot
 
-/- warning: ideal.jacobson_eq_iff_jacobson_quotient_eq_bot -> Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_botₓ'. -/
 /-- An ideal `I` of `R` is equal to its Jacobson radical if and only if
 the Jacobson radical of the quotient ring `R/I` is the zero ideal -/
 theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
@@ -419,9 +314,6 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
     simpa using h
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
 
-/- warning: ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot -> Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_botₓ'. -/
 /-- The standard radical and Jacobson radical of an ideal `I` of `R` are equal if and only if
 the nilradical and Jacobson radical of the quotient ring `R/I` coincide -/
 theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
@@ -459,9 +351,6 @@ open Polynomial
 
 variable [CommRing R]
 
-/- warning: ideal.jacobson_bot_polynomial_le_Inf_map_maximal -> Ideal.jacobson_bot_polynomial_le_sInf_map_maximal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximalₓ'. -/
 theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
   by
@@ -479,12 +368,6 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     eq_C_of_degree_eq_zero (degree_eq_zero_of_is_unit ((mem_jacobson_bot.1 hf) X))
 #align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximal
 
-/- warning: ideal.jacobson_bot_polynomial_of_jacobson_bot -> Ideal.jacobson_bot_polynomial_of_jacobson_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) -> (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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)))))) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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)))))) -> (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align ideal.jacobson_bot_polynomial_of_jacobson_bot Ideal.jacobson_bot_polynomial_of_jacobson_botₓ'. -/
 theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) = ⊥) :
     jacobson (⊥ : Ideal R[X]) = ⊥ :=
   by
@@ -522,24 +405,12 @@ theorem isLocal_of_isMaximal_radical {I : Ideal R} (hi : IsMaximal (radical I))
 #align ideal.is_local_of_is_maximal_radical Ideal.isLocal_of_isMaximal_radical
 -/
 
-/- warning: ideal.is_local.le_jacobson -> Ideal.IsLocal.le_jacobson 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))}, (Ideal.IsLocal.{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))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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) -> (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{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)))))) -> (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))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))))) J (Ideal.jacobson.{u1} R (CommRing.toRing.{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))} {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ideal.IsLocal.{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)))))))) I J) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) J (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{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)))))) -> (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)))))))) J (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I))
-Case conversion may be inaccurate. Consider using '#align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobsonₓ'. -/
 theorem IsLocal.le_jacobson {I J : Ideal R} (hi : IsLocal I) (hij : I ≤ J) (hj : J ≠ ⊤) :
     J ≤ jacobson I :=
   let ⟨M, hm, hjm⟩ := exists_le_maximal J hj
   le_trans hjm <| le_of_eq <| Eq.symm <| hi.1.eq_of_le hm.1.1 <| sInf_le ⟨le_trans hij hjm, hm⟩
 #align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobson
 
-/- warning: ideal.is_local.mem_jacobson_or_exists_inv -> Ideal.IsLocal.mem_jacobson_or_exists_inv 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))}, (Ideal.IsLocal.{u1} R _inst_1 I) -> (forall (x : R), Or (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Exists.{succ u1} R (fun (y : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y x) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{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))}, (Ideal.IsLocal.{u1} R _inst_1 I) -> (forall (x : R), Or (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Exists.{succ u1} R (fun (y : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) y x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) I)))
-Case conversion may be inaccurate. Consider using '#align ideal.is_local.mem_jacobson_or_exists_inv Ideal.IsLocal.mem_jacobson_or_exists_invₓ'. -/
 theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R) :
     x ∈ jacobson I ∨ ∃ y, y * x - 1 ∈ I :=
   by_cases

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

@@ -400,10 +400,7 @@ theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsU
 #align ideal.mem_jacobson_bot Ideal.mem_jacobson_bot
 
 /- warning: ideal.jacobson_eq_iff_jacobson_quotient_eq_bot -> Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot 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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I) I) (Eq.{succ 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.jacobson.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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))))))) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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)))))))
-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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I) I) (Eq.{succ 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) (Ring.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.toRing.{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.jacobson.{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.toRing.{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)) (Bot.bot.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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)))))) (Semiring.toModule.{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))))))) (Bot.bot.{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) (Ring.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.toRing.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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) (Ring.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.toRing.{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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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) (Ring.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.toRing.{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)))))) (Semiring.toModule.{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) (Ring.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.toRing.{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)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_botₓ'. -/
 /-- An ideal `I` of `R` is equal to its Jacobson radical if and only if
 the Jacobson radical of the quotient ring `R/I` is the zero ideal -/
@@ -423,10 +420,7 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
 
 /- warning: ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot -> Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot 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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Eq.{succ 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) (CommSemiring.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.toCommSemiring.{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.radical.{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.toCommSemiring.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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.jacobson.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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))))))))
-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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Eq.{succ 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.radical.{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)) (Bot.bot.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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)))))) (Semiring.toModule.{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.jacobson.{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.toRing.{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)) (Bot.bot.{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) (Ring.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.toRing.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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) (Ring.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.toRing.{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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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) (Ring.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.toRing.{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)))))) (Semiring.toModule.{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) (Ring.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.toRing.{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))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_botₓ'. -/
 /-- The standard radical and Jacobson radical of an ideal `I` of `R` are equal if and only if
 the nilradical and Jacobson radical of the quotient ring `R/I` coincide -/
@@ -466,10 +460,7 @@ open Polynomial
 variable [CommRing R]
 
 /- warning: ideal.jacobson_bot_polynomial_le_Inf_map_maximal -> Ideal.jacobson_bot_polynomial_le_sInf_map_maximal is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], LE.le.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Preorder.toHasLe.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InfSet.sInf.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasInf.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Set.image.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (setOf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) J))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], LE.le.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Preorder.toLE.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.completeLattice.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (InfSet.sInf.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instInfSetSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Set.image.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (setOf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) J))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximalₓ'. -/
 theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
 
 ! This file was ported from Lean 3 source module ring_theory.jacobson_ideal
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Polynomial.Quotient
 /-!
 # Jacobson radical
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The Jacobson radical of a ring `R` is defined to be the intersection of all maximal ideals of `R`.
 This is similar to how the nilradical is equal to the intersection of all prime ideals of `R`.
 

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

@@ -256,7 +256,7 @@ theorem eq_jacobson_iff_not_mem :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
 Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjectiveₓ'. -/
 theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) :
     RingHom.ker f ≤ I → map f I.jacobson = (map f I).jacobson :=
@@ -281,7 +281,7 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))}, (Function.Bijective.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Bijective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Bijective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
 Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijectiveₓ'. -/
 theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
     map f I.jacobson = (map f I).jacobson :=
@@ -304,7 +304,7 @@ theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f K)))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f K)))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f K)))
 Case conversion may be inaccurate. Consider using '#align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjectiveₓ'. -/
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :
     comap f K.jacobson = (comap f K).jacobson :=

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

@@ -58,24 +58,46 @@ section Ring
 
 variable [Ring R] [Ring S] {I : Ideal R}
 
+#print Ideal.jacobson /-
 /-- The Jacobson radical of `I` is the infimum of all maximal (left) ideals containing `I`. -/
 def jacobson (I : Ideal R) : Ideal R :=
   sInf { J : Ideal R | I ≤ J ∧ IsMaximal J }
 #align ideal.jacobson Ideal.jacobson
+-/
 
+/- warning: ideal.le_jacobson -> Ideal.le_jacobson is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I (Ideal.jacobson.{u1} R _inst_1 I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I (Ideal.jacobson.{u1} R _inst_1 I)
+Case conversion may be inaccurate. Consider using '#align ideal.le_jacobson Ideal.le_jacobsonₓ'. -/
 theorem le_jacobson : I ≤ jacobson I := fun x hx => mem_sInf.mpr fun J hJ => hJ.left hx
 #align ideal.le_jacobson Ideal.le_jacobson
 
+#print Ideal.jacobson_idem /-
 @[simp]
 theorem jacobson_idem : jacobson (jacobson I) = jacobson I :=
   le_antisymm (sInf_le_sInf fun J hJ => ⟨sInf_le hJ, hJ.2⟩) le_jacobson
 #align ideal.jacobson_idem Ideal.jacobson_idem
+-/
 
+/- warning: ideal.jacobson_top -> Ideal.jacobson_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_top Ideal.jacobson_topₓ'. -/
 @[simp]
 theorem jacobson_top : jacobson (⊤ : Ideal R) = ⊤ :=
   eq_top_iff.2 le_jacobson
 #align ideal.jacobson_top Ideal.jacobson_top
 
+/- warning: ideal.jacobson_eq_top_iff -> Ideal.jacobson_eq_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iffₓ'. -/
 @[simp]
 theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
   ⟨fun H =>
@@ -88,18 +110,34 @@ theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
     fun H => eq_top_iff.2 <| le_sInf fun J ⟨hij, hj⟩ => H ▸ hij⟩
 #align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iff
 
+/- warning: ideal.jacobson_eq_bot -> Ideal.jacobson_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instBotSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_eq_bot Ideal.jacobson_eq_botₓ'. -/
 theorem jacobson_eq_bot : jacobson I = ⊥ → I = ⊥ := fun h => eq_bot_iff.mpr (h ▸ le_jacobson)
 #align ideal.jacobson_eq_bot Ideal.jacobson_eq_bot
 
+#print Ideal.jacobson_eq_self_of_isMaximal /-
 theorem jacobson_eq_self_of_isMaximal [H : IsMaximal I] : I.jacobson = I :=
   le_antisymm (sInf_le ⟨le_of_eq rfl, H⟩) le_jacobson
 #align ideal.jacobson_eq_self_of_is_maximal Ideal.jacobson_eq_self_of_isMaximal
+-/
 
+#print Ideal.jacobson.isMaximal /-
 instance (priority := 100) jacobson.isMaximal [H : IsMaximal I] : IsMaximal (jacobson I) :=
   ⟨⟨fun htop => H.1.1 (jacobson_eq_top_iff.1 htop), fun J hJ =>
       H.1.2 _ (lt_of_le_of_lt le_jacobson hJ)⟩⟩
 #align ideal.jacobson.is_maximal Ideal.jacobson.isMaximal
+-/
 
+/- warning: ideal.mem_jacobson_iff -> Ideal.mem_jacobson_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {x : R}, Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Ideal.jacobson.{u1} R _inst_1 I)) (forall (y : R), Exists.{succ u1} R (fun (z : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) z y) x) z) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) I))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {x : R}, Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x (Ideal.jacobson.{u1} R _inst_1 I)) (forall (y : R), Exists.{succ u1} R (fun (z : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) z y) x) z) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) I))
+Case conversion may be inaccurate. Consider using '#align ideal.mem_jacobson_iff Ideal.mem_jacobson_iffₓ'. -/
 theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x + z - 1 ∈ I :=
   ⟨fun hx y =>
     by_cases
@@ -133,6 +171,12 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
                 (him hz)⟩
 #align ideal.mem_jacobson_iff Ideal.mem_jacobson_iff
 
+/- warning: ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson -> Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} (r : R), (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) r (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (Ideal.jacobson.{u1} R _inst_1 I)) -> (Exists.{succ u1} R (fun (s : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) s r) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) I))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} (r : R), (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) r (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Ideal.jacobson.{u1} R _inst_1 I)) -> (Exists.{succ u1} R (fun (s : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) s r) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) I))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobsonₓ'. -/
 theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r - 1 ∈ jacobson I) :
     ∃ s, s * r - 1 ∈ I := by
   cases' mem_jacobson_iff.1 h 1 with s hs
@@ -140,6 +184,12 @@ theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r
   simpa [mul_sub] using hs
 #align ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson
 
+/- warning: ideal.eq_jacobson_iff_Inf_maximal -> Ideal.eq_jacobson_iff_sInf_maximal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (Or (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) J) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (Or (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) J) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
+Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximalₓ'. -/
 /-- An ideal equals its Jacobson radical iff it is the intersection of a set of maximal ideals.
 Allowing the set to include ⊤ is equivalent, and is included only to simplify some proofs. -/
 theorem eq_jacobson_iff_sInf_maximal :
@@ -155,6 +205,12 @@ theorem eq_jacobson_iff_sInf_maximal :
   · exact is_top.symm ▸ Submodule.mem_top
 #align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximal
 
+/- warning: ideal.eq_jacobson_iff_Inf_maximal' -> Ideal.eq_jacobson_iff_sInf_maximal' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.Mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.hasMem.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (forall (K : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) J K) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) K (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (Exists.{succ u1} (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (fun (M : Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) => And (forall (J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (Membership.mem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Set.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.instMembershipSet.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1))) J M) -> (forall (K : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)), (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLT.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) J K) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) K (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M))))
+Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'ₓ'. -/
 theorem eq_jacobson_iff_sInf_maximal' :
     I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, ∀ (K : Ideal R), J < K → K = ⊤) ∧ I = sInf M :=
   eq_jacobson_iff_sInf_maximal.trans
@@ -172,6 +228,12 @@ theorem eq_jacobson_iff_sInf_maximal' :
           hM.2⟩⟩⟩
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 
+/- warning: ideal.eq_jacobson_iff_not_mem -> Ideal.eq_jacobson_iff_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (forall (x : R), (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x I)) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (fun (M : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) => And (And (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I M) (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) M)) (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x M)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.jacobson.{u1} R _inst_1 I) I) (forall (x : R), (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x I)) -> (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (fun (M : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) => And (And (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I M) (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R _inst_1) M)) (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) x M)))))
+Case conversion may be inaccurate. Consider using '#align ideal.eq_jacobson_iff_not_mem Ideal.eq_jacobson_iff_not_memₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
@@ -190,6 +252,12 @@ theorem eq_jacobson_iff_not_mem :
     exact h x hx
 #align ideal.eq_jacobson_iff_not_mem Ideal.eq_jacobson_iff_not_mem
 
+/- warning: ideal.map_jacobson_of_surjective -> Ideal.map_jacobson_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) I) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
+Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjectiveₓ'. -/
 theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) :
     RingHom.ker f ≤ I → map f I.jacobson = (map f I).jacobson :=
   by
@@ -209,17 +277,35 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     · exact Set.mem_insert_of_mem ⊤ ⟨map_mono hJ.1.1, hmax⟩
 #align ideal.map_jacobson_of_surjective Ideal.map_jacobson_of_surjective
 
+/- warning: ideal.map_jacobson_of_bijective -> Ideal.map_jacobson_of_bijective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))}, (Function.Bijective.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f I)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Bijective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u1} R _inst_1 I)) (Ideal.jacobson.{u2} S _inst_2 (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f I)))
+Case conversion may be inaccurate. Consider using '#align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijectiveₓ'. -/
 theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
     map f I.jacobson = (map f I).jacobson :=
   map_jacobson_of_surjective hf.right
     (le_trans (le_of_eq (f.injective_iff_ker_eq_bot.1 hf.left)) bot_le)
 #align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijective
 
+/- warning: ideal.comap_jacobson -> Ideal.comap_jacobson is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))} {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.hasInf.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.image.{u2, u1} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f) (setOf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (fun (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) => And (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (SetLike.partialOrder.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) K J) (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S _inst_2) J)))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))} {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (InfSet.sInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.instInfSetSubmodule.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Set.image.{u2, u1} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f) (setOf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (fun (J : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) => And (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Preorder.toLE.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_2))))))) K J) (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S _inst_2) J)))))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_jacobson Ideal.comap_jacobsonₓ'. -/
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
     comap f K.jacobson = sInf (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
   trans (comap_sInf' f _) sInf_eq_iInf.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
 
+/- warning: ideal.comap_jacobson_of_surjective -> Ideal.comap_jacobson_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{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 _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f K)))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Ring.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))}, (Function.Surjective.{succ u1, succ u2} R S (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2)))))) f)) -> (forall {K : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_2)}, Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f (Ideal.jacobson.{u2} S _inst_2 K)) (Ideal.jacobson.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) f K)))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjectiveₓ'. -/
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :
     comap f K.jacobson = (comap f K).jacobson :=
   by
@@ -244,6 +330,12 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
     refine' sInf_le ⟨comap_mono hJ.left, comap_is_maximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective
 
+/- warning: ideal.jacobson_mono -> Ideal.jacobson_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) I J) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ideal.jacobson.{u1} R _inst_1 I) (Ideal.jacobson.{u1} R _inst_1 J))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) I J) -> (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Ideal.jacobson.{u1} R _inst_1 I) (Ideal.jacobson.{u1} R _inst_1 J))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_mono Ideal.jacobson_monoₓ'. -/
 @[mono]
 theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson :=
   by
@@ -258,14 +350,28 @@ section CommRing
 
 variable [CommRing R] [CommRing S] {I : Ideal R}
 
+/- warning: ideal.radical_le_jacobson -> Ideal.radical_le_jacobson 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))}, LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{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))}, 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)))))))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)
+Case conversion may be inaccurate. Consider using '#align ideal.radical_le_jacobson Ideal.radical_le_jacobsonₓ'. -/
 theorem radical_le_jacobson : radical I ≤ jacobson I :=
   le_sInf fun J hJ => (radical_eq_sInf I).symm ▸ sInf_le ⟨hJ.left, IsMaximal.isPrime hJ.right⟩
 #align ideal.radical_le_jacobson Ideal.radical_le_jacobson
 
+#print Ideal.isRadical_of_eq_jacobson /-
 theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
   radical_le_jacobson.trans h.le
 #align ideal.is_radical_of_eq_jacobson Ideal.isRadical_of_eq_jacobson
+-/
 
+/- warning: ideal.is_unit_of_sub_one_mem_jacobson_bot -> Ideal.isUnit_of_sub_one_mem_jacobson_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (r : R), (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) r (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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))))))) -> (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) r)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (r : R), (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) r (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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))))))) -> (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) r)
+Case conversion may be inaccurate. Consider using '#align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_botₓ'. -/
 theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥ : Ideal R)) :
     IsUnit r := by
   cases' exists_mul_sub_mem_of_sub_one_mem_jacobson r h with s hs
@@ -273,6 +379,12 @@ theorem isUnit_of_sub_one_mem_jacobson_bot (r : R) (h : r - 1 ∈ jacobson (⊥
   exact isUnit_of_mul_eq_one _ _ hs
 #align ideal.is_unit_of_sub_one_mem_jacobson_bot Ideal.isUnit_of_sub_one_mem_jacobson_bot
 
+/- warning: ideal.mem_jacobson_bot -> Ideal.mem_jacobson_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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))))))) (forall (y : R), IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x y) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {x : R}, Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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))))))) (forall (y : R), IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x y) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.mem_jacobson_bot Ideal.mem_jacobson_botₓ'. -/
 theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsUnit (x * y + 1) :=
   ⟨fun hx y =>
     let ⟨z, hz⟩ := (mem_jacobson_iff.1 hx) y
@@ -284,6 +396,12 @@ theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsU
       ⟨b, (Submodule.mem_bot R).2 (hb ▸ by ring)⟩⟩
 #align ideal.mem_jacobson_bot Ideal.mem_jacobson_bot
 
+/- warning: ideal.jacobson_eq_iff_jacobson_quotient_eq_bot -> Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot 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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I) I) (Eq.{succ 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.jacobson.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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))))))) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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)))))))
+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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I) I) (Eq.{succ 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) (Ring.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.toRing.{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.jacobson.{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.toRing.{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)) (Bot.bot.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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)))))) (Semiring.toModule.{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))))))) (Bot.bot.{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) (Ring.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.toRing.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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) (Ring.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.toRing.{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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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) (Ring.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.toRing.{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)))))) (Semiring.toModule.{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) (Ring.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.toRing.{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.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_botₓ'. -/
 /-- An ideal `I` of `R` is equal to its Jacobson radical if and only if
 the Jacobson radical of the quotient ring `R/I` is the zero ideal -/
 theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
@@ -301,6 +419,12 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
     simpa using h
 #align ideal.jacobson_eq_iff_jacobson_quotient_eq_bot Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot
 
+/- warning: ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot -> Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot 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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Eq.{succ 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) (CommSemiring.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.toCommSemiring.{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.radical.{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.toCommSemiring.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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.jacobson.{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)) (Bot.bot.{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)))) (Submodule.hasBot.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (Semiring.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.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)))))) (Semiring.toModule.{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))))))))
+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))}, Iff (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.radical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) I) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Eq.{succ 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.radical.{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)) (Bot.bot.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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)))))) (Semiring.toModule.{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.jacobson.{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.toRing.{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)) (Bot.bot.{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) (Ring.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.toRing.{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)))) (Submodule.instBotSubmodule.{u1, 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) (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) (Ring.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.toRing.{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))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) (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) (Ring.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.toRing.{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)))))) (Semiring.toModule.{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) (Ring.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.toRing.{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.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_botₓ'. -/
 /-- The standard radical and Jacobson radical of an ideal `I` of `R` are equal if and only if
 the nilradical and Jacobson radical of the quotient ring `R/I` coincide -/
 theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
@@ -319,12 +443,14 @@ theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
     simpa using this
 #align ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot
 
+#print Ideal.jacobson_radical_eq_jacobson /-
 theorem jacobson_radical_eq_jacobson : I.radical.jacobson = I.jacobson :=
   le_antisymm
     (le_trans (le_of_eq (congr_arg jacobson (radical_eq_sInf I)))
       (sInf_le_sInf fun J hJ => ⟨sInf_le ⟨hJ.1, hJ.2.IsPrime⟩, hJ.2⟩))
     (jacobson_mono le_radical)
 #align ideal.jacobson_radical_eq_jacobson Ideal.jacobson_radical_eq_jacobson
+-/
 
 end CommRing
 
@@ -336,6 +462,12 @@ open Polynomial
 
 variable [CommRing R]
 
+/- warning: ideal.jacobson_bot_polynomial_le_Inf_map_maximal -> Ideal.jacobson_bot_polynomial_le_sInf_map_maximal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], LE.le.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Preorder.toHasLe.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (InfSet.sInf.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasInf.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Set.image.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (setOf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) J))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], LE.le.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Preorder.toLE.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.completeLattice.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (InfSet.sInf.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instInfSetSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Set.image.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (setOf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) J))))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximalₓ'. -/
 theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
   by
@@ -353,6 +485,12 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
     eq_C_of_degree_eq_zero (degree_eq_zero_of_is_unit ((mem_jacobson_bot.1 hf) X))
 #align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximal
 
+/- warning: ideal.jacobson_bot_polynomial_of_jacobson_bot -> Ideal.jacobson_bot_polynomial_of_jacobson_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) -> (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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)))))) (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.instBotSubmodule.{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)))))) -> (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ideal.jacobson.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Submodule.instBotSubmodule.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.jacobson_bot_polynomial_of_jacobson_bot Ideal.jacobson_bot_polynomial_of_jacobson_botₓ'. -/
 theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) = ⊥) :
     jacobson (⊥ : Ideal R[X]) = ⊥ :=
   by
@@ -368,28 +506,46 @@ section IsLocal
 
 variable [CommRing R]
 
+#print Ideal.IsLocal /-
 /-- An ideal `I` is local iff its Jacobson radical is maximal. -/
 class IsLocal (I : Ideal R) : Prop where
   out : IsMaximal (jacobson I)
 #align ideal.is_local Ideal.IsLocal
+-/
 
+#print Ideal.isLocal_iff /-
 theorem isLocal_iff {I : Ideal R} : IsLocal I ↔ IsMaximal (jacobson I) :=
   ⟨fun h => h.1, fun h => ⟨h⟩⟩
 #align ideal.is_local_iff Ideal.isLocal_iff
+-/
 
+#print Ideal.isLocal_of_isMaximal_radical /-
 theorem isLocal_of_isMaximal_radical {I : Ideal R} (hi : IsMaximal (radical I)) : IsLocal I :=
   ⟨have : radical I = jacobson I :=
       le_antisymm (le_sInf fun M ⟨him, hm⟩ => hm.IsPrime.radical_le_iff.2 him)
         (sInf_le ⟨le_radical, hi⟩)
     show IsMaximal (jacobson I) from this ▸ hi⟩
 #align ideal.is_local_of_is_maximal_radical Ideal.isLocal_of_isMaximal_radical
+-/
 
+/- warning: ideal.is_local.le_jacobson -> Ideal.IsLocal.le_jacobson 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))}, (Ideal.IsLocal.{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))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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) -> (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) J (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{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)))))) -> (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))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))))) J (Ideal.jacobson.{u1} R (CommRing.toRing.{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))} {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ideal.IsLocal.{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)))))))) I J) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) J (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{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)))))) -> (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)))))))) J (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I))
+Case conversion may be inaccurate. Consider using '#align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobsonₓ'. -/
 theorem IsLocal.le_jacobson {I J : Ideal R} (hi : IsLocal I) (hij : I ≤ J) (hj : J ≠ ⊤) :
     J ≤ jacobson I :=
   let ⟨M, hm, hjm⟩ := exists_le_maximal J hj
   le_trans hjm <| le_of_eq <| Eq.symm <| hi.1.eq_of_le hm.1.1 <| sInf_le ⟨le_trans hij hjm, hm⟩
 #align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobson
 
+/- warning: ideal.is_local.mem_jacobson_or_exists_inv -> Ideal.IsLocal.mem_jacobson_or_exists_inv 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))}, (Ideal.IsLocal.{u1} R _inst_1 I) -> (forall (x : R), Or (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Exists.{succ u1} R (fun (y : R) => Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y x) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{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))}, (Ideal.IsLocal.{u1} R _inst_1 I) -> (forall (x : R), Or (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{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))))) x (Ideal.jacobson.{u1} R (CommRing.toRing.{u1} R _inst_1) I)) (Exists.{succ u1} R (fun (y : R) => Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) y x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) I)))
+Case conversion may be inaccurate. Consider using '#align ideal.is_local.mem_jacobson_or_exists_inv Ideal.IsLocal.mem_jacobson_or_exists_invₓ'. -/
 theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R) :
     x ∈ jacobson I ∨ ∃ y, y * x - 1 ∈ I :=
   by_cases
@@ -404,6 +560,7 @@ theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R
 
 end IsLocal
 
+#print Ideal.isPrimary_of_isMaximal_radical /-
 theorem isPrimary_of_isMaximal_radical [CommRing R] {I : Ideal R} (hi : IsMaximal (radical I)) :
     IsPrimary I :=
   have : radical I = jacobson I :=
@@ -416,6 +573,7 @@ theorem isPrimary_of_isMaximal_radical [CommRing R] {I : Ideal R} (hi : IsMaxima
           exact I.sub_mem (I.mul_mem_left _ hxy) (I.mul_mem_left _ hz))
       (this ▸ id)⟩
 #align ideal.is_primary_of_is_maximal_radical Ideal.isPrimary_of_isMaximal_radical
+-/
 
 end Ideal
 

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

@@ -60,15 +60,15 @@ variable [Ring R] [Ring S] {I : Ideal R}
 
 /-- The Jacobson radical of `I` is the infimum of all maximal (left) ideals containing `I`. -/
 def jacobson (I : Ideal R) : Ideal R :=
-  infₛ { J : Ideal R | I ≤ J ∧ IsMaximal J }
+  sInf { J : Ideal R | I ≤ J ∧ IsMaximal J }
 #align ideal.jacobson Ideal.jacobson
 
-theorem le_jacobson : I ≤ jacobson I := fun x hx => mem_infₛ.mpr fun J hJ => hJ.left hx
+theorem le_jacobson : I ≤ jacobson I := fun x hx => mem_sInf.mpr fun J hJ => hJ.left hx
 #align ideal.le_jacobson Ideal.le_jacobson
 
 @[simp]
 theorem jacobson_idem : jacobson (jacobson I) = jacobson I :=
-  le_antisymm (infₛ_le_infₛ fun J hJ => ⟨infₛ_le hJ, hJ.2⟩) le_jacobson
+  le_antisymm (sInf_le_sInf fun J hJ => ⟨sInf_le hJ, hJ.2⟩) le_jacobson
 #align ideal.jacobson_idem Ideal.jacobson_idem
 
 @[simp]
@@ -82,17 +82,17 @@ theorem jacobson_eq_top_iff : jacobson I = ⊤ ↔ I = ⊤ :=
     by_contradiction fun hi =>
       let ⟨M, hm, him⟩ := exists_le_maximal I hi
       lt_top_iff_ne_top.1
-        (lt_of_le_of_lt (show jacobson I ≤ M from infₛ_le ⟨him, hm⟩) <|
+        (lt_of_le_of_lt (show jacobson I ≤ M from sInf_le ⟨him, hm⟩) <|
           lt_top_iff_ne_top.2 hm.ne_top)
         H,
-    fun H => eq_top_iff.2 <| le_infₛ fun J ⟨hij, hj⟩ => H ▸ hij⟩
+    fun H => eq_top_iff.2 <| le_sInf fun J ⟨hij, hj⟩ => H ▸ hij⟩
 #align ideal.jacobson_eq_top_iff Ideal.jacobson_eq_top_iff
 
 theorem jacobson_eq_bot : jacobson I = ⊥ → I = ⊥ := fun h => eq_bot_iff.mpr (h ▸ le_jacobson)
 #align ideal.jacobson_eq_bot Ideal.jacobson_eq_bot
 
 theorem jacobson_eq_self_of_isMaximal [H : IsMaximal I] : I.jacobson = I :=
-  le_antisymm (infₛ_le ⟨le_of_eq rfl, H⟩) le_jacobson
+  le_antisymm (sInf_le ⟨le_of_eq rfl, H⟩) le_jacobson
 #align ideal.jacobson_eq_self_of_is_maximal Ideal.jacobson_eq_self_of_isMaximal
 
 instance (priority := 100) jacobson.isMaximal [H : IsMaximal I] : IsMaximal (jacobson I) :=
@@ -111,14 +111,14 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
             exact I.neg_mem hpi⟩)
       fun hxy : I ⊔ span {y * x + 1} ≠ ⊤ =>
       let ⟨M, hm1, hm2⟩ := exists_le_maximal _ hxy
-      suffices x ∉ M from (this <| mem_infₛ.1 hx ⟨le_trans le_sup_left hm2, hm1⟩).elim
+      suffices x ∉ M from (this <| mem_sInf.1 hx ⟨le_trans le_sup_left hm2, hm1⟩).elim
       fun hxm =>
       hm1.1.1 <|
         (eq_top_iff_one _).2 <|
           add_sub_cancel' (y * x) 1 ▸
             M.sub_mem (le_sup_right.trans hm2 <| subset_span rfl) (M.mul_mem_left _ hxm),
     fun hx =>
-    mem_infₛ.2 fun M ⟨him, hm⟩ =>
+    mem_sInf.2 fun M ⟨him, hm⟩ =>
       by_contradiction fun hxm =>
         let ⟨y, i, hi, df⟩ := hm.exists_inv hxm
         let ⟨z, hz⟩ := hx (-y)
@@ -142,8 +142,8 @@ theorem exists_mul_sub_mem_of_sub_one_mem_jacobson {I : Ideal R} (r : R) (h : r
 
 /-- An ideal equals its Jacobson radical iff it is the intersection of a set of maximal ideals.
 Allowing the set to include ⊤ is equivalent, and is included only to simplify some proofs. -/
-theorem eq_jacobson_iff_infₛ_maximal :
-    I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, IsMaximal J ∨ J = ⊤) ∧ I = infₛ M :=
+theorem eq_jacobson_iff_sInf_maximal :
+    I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, IsMaximal J ∨ J = ⊤) ∧ I = sInf M :=
   by
   use fun hI => ⟨{ J : Ideal R | I ≤ J ∧ J.IsMaximal }, ⟨fun _ hJ => Or.inl hJ.right, hI.symm⟩⟩
   rintro ⟨M, hM, hInf⟩
@@ -151,13 +151,13 @@ theorem eq_jacobson_iff_infₛ_maximal :
   rw [hInf, mem_Inf]
   intro I hI
   cases' hM I hI with is_max is_top
-  · exact (mem_Inf.1 hx) ⟨le_infₛ_iff.1 (le_of_eq hInf) I hI, IsMax⟩
+  · exact (mem_Inf.1 hx) ⟨le_sInf_iff.1 (le_of_eq hInf) I hI, IsMax⟩
   · exact is_top.symm ▸ Submodule.mem_top
-#align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_infₛ_maximal
+#align ideal.eq_jacobson_iff_Inf_maximal Ideal.eq_jacobson_iff_sInf_maximal
 
-theorem eq_jacobson_iff_infₛ_maximal' :
-    I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, ∀ (K : Ideal R), J < K → K = ⊤) ∧ I = infₛ M :=
-  eq_jacobson_iff_infₛ_maximal.trans
+theorem eq_jacobson_iff_sInf_maximal' :
+    I.jacobson = I ↔ ∃ M : Set (Ideal R), (∀ J ∈ M, ∀ (K : Ideal R), J < K → K = ⊤) ∧ I = sInf M :=
+  eq_jacobson_iff_sInf_maximal.trans
     ⟨fun h =>
       let ⟨M, hM⟩ := h
       ⟨M,
@@ -170,7 +170,7 @@ theorem eq_jacobson_iff_infₛ_maximal' :
         ⟨fun J hJ =>
           Or.rec_on (Classical.em (J = ⊤)) (fun h => Or.inr h) fun h => Or.inl ⟨⟨h, hM.1 J hJ⟩⟩,
           hM.2⟩⟩⟩
-#align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_infₛ_maximal'
+#align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_sInf_maximal'
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
@@ -198,11 +198,11 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
   have : ∀ J ∈ { J : Ideal R | I ≤ J ∧ J.IsMaximal }, f.ker ≤ J := fun J hJ => le_trans h hJ.left
   refine' trans (map_Inf hf this) (le_antisymm _ _)
   · refine'
-      infₛ_le_infₛ fun J hJ =>
+      sInf_le_sInf fun J hJ =>
         ⟨comap f J, ⟨⟨le_comap_of_map_le hJ.1, _⟩, map_comap_of_surjective f hf J⟩⟩
     haveI : J.is_maximal := hJ.right
     exact comap_is_maximal_of_surjective f hf
-  · refine' infₛ_le_infₛ_of_subset_insert_top fun j hj => hj.recOn fun J hJ => _
+  · refine' sInf_le_sInf_of_subset_insert_top fun j hj => hj.recOn fun J hJ => _
     rw [← hJ.2]
     cases' map_eq_top_or_is_maximal_of_surjective f hf hJ.left.right with htop hmax
     · exact htop.symm ▸ Set.mem_insert ⊤ _
@@ -216,8 +216,8 @@ theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
 #align ideal.map_jacobson_of_bijective Ideal.map_jacobson_of_bijective
 
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
-    comap f K.jacobson = infₛ (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
-  trans (comap_infₛ' f _) infₛ_eq_infᵢ.symm
+    comap f K.jacobson = sInf (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
+  trans (comap_sInf' f _) sInf_eq_iInf.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
 
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :
@@ -226,8 +226,8 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
   unfold Ideal.jacobson
   refine' le_antisymm _ _
   · refine' le_trans (comap_mono (le_of_eq (trans top_inf_eq.symm Inf_insert.symm))) _
-    rw [comap_Inf', infₛ_eq_infᵢ]
-    refine' infᵢ_le_infᵢ_of_subset fun J hJ => _
+    rw [comap_Inf', sInf_eq_iInf]
+    refine' iInf_le_iInf_of_subset fun J hJ => _
     have : comap f (map f J) = J :=
       trans (comap_map_of_surjective f hf J)
         (le_antisymm (sup_le_iff.2 ⟨le_of_eq rfl, le_trans (comap_mono bot_le) hJ.left⟩)
@@ -239,9 +239,9 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
         ⟨map f J,
           ⟨Set.mem_insert_of_mem _ ⟨le_map_of_comap_le_of_surjective f hf hJ.1, hmax⟩, this⟩⟩
   · rw [comap_Inf]
-    refine' le_infᵢ_iff.2 fun J => le_infᵢ_iff.2 fun hJ => _
+    refine' le_iInf_iff.2 fun J => le_iInf_iff.2 fun hJ => _
     haveI : J.is_maximal := hJ.right
-    refine' infₛ_le ⟨comap_mono hJ.left, comap_is_maximal_of_surjective _ hf⟩
+    refine' sInf_le ⟨comap_mono hJ.left, comap_is_maximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective
 
 @[mono]
@@ -259,7 +259,7 @@ section CommRing
 variable [CommRing R] [CommRing S] {I : Ideal R}
 
 theorem radical_le_jacobson : radical I ≤ jacobson I :=
-  le_infₛ fun J hJ => (radical_eq_infₛ I).symm ▸ infₛ_le ⟨hJ.left, IsMaximal.isPrime hJ.right⟩
+  le_sInf fun J hJ => (radical_eq_sInf I).symm ▸ sInf_le ⟨hJ.left, IsMaximal.isPrime hJ.right⟩
 #align ideal.radical_le_jacobson Ideal.radical_le_jacobson
 
 theorem isRadical_of_eq_jacobson (h : jacobson I = I) : I.IsRadical :=
@@ -321,8 +321,8 @@ theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
 
 theorem jacobson_radical_eq_jacobson : I.radical.jacobson = I.jacobson :=
   le_antisymm
-    (le_trans (le_of_eq (congr_arg jacobson (radical_eq_infₛ I)))
-      (infₛ_le_infₛ fun J hJ => ⟨infₛ_le ⟨hJ.1, hJ.2.IsPrime⟩, hJ.2⟩))
+    (le_trans (le_of_eq (congr_arg jacobson (radical_eq_sInf I)))
+      (sInf_le_sInf fun J hJ => ⟨sInf_le ⟨hJ.1, hJ.2.IsPrime⟩, hJ.2⟩))
     (jacobson_mono le_radical)
 #align ideal.jacobson_radical_eq_jacobson Ideal.jacobson_radical_eq_jacobson
 
@@ -336,10 +336,10 @@ open Polynomial
 
 variable [CommRing R]
 
-theorem jacobson_bot_polynomial_le_infₛ_map_maximal :
-    jacobson (⊥ : Ideal R[X]) ≤ infₛ (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
+theorem jacobson_bot_polynomial_le_sInf_map_maximal :
+    jacobson (⊥ : Ideal R[X]) ≤ sInf (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
   by
-  refine' le_infₛ fun J => exists_imp.2 fun j hj => _
+  refine' le_sInf fun J => exists_imp.2 fun j hj => _
   haveI : j.is_maximal := hj.1
   refine' trans (jacobson_mono bot_le) (le_of_eq _ : J.jacobson ≤ J)
   suffices (⊥ : Ideal (Polynomial (R ⧸ j))).jacobson = ⊥
@@ -351,7 +351,7 @@ theorem jacobson_bot_polynomial_le_infₛ_map_maximal :
   refine' eq_bot_iff.2 fun f hf => _
   simpa [(fun hX => by simpa using congr_arg (fun f => coeff f 1) hX : (X : (R ⧸ j)[X]) ≠ 0)] using
     eq_C_of_degree_eq_zero (degree_eq_zero_of_is_unit ((mem_jacobson_bot.1 hf) X))
-#align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_infₛ_map_maximal
+#align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximal
 
 theorem jacobson_bot_polynomial_of_jacobson_bot (h : jacobson (⊥ : Ideal R) = ⊥) :
     jacobson (⊥ : Ideal R[X]) = ⊥ :=
@@ -379,15 +379,15 @@ theorem isLocal_iff {I : Ideal R} : IsLocal I ↔ IsMaximal (jacobson I) :=
 
 theorem isLocal_of_isMaximal_radical {I : Ideal R} (hi : IsMaximal (radical I)) : IsLocal I :=
   ⟨have : radical I = jacobson I :=
-      le_antisymm (le_infₛ fun M ⟨him, hm⟩ => hm.IsPrime.radical_le_iff.2 him)
-        (infₛ_le ⟨le_radical, hi⟩)
+      le_antisymm (le_sInf fun M ⟨him, hm⟩ => hm.IsPrime.radical_le_iff.2 him)
+        (sInf_le ⟨le_radical, hi⟩)
     show IsMaximal (jacobson I) from this ▸ hi⟩
 #align ideal.is_local_of_is_maximal_radical Ideal.isLocal_of_isMaximal_radical
 
 theorem IsLocal.le_jacobson {I J : Ideal R} (hi : IsLocal I) (hij : I ≤ J) (hj : J ≠ ⊤) :
     J ≤ jacobson I :=
   let ⟨M, hm, hjm⟩ := exists_le_maximal J hj
-  le_trans hjm <| le_of_eq <| Eq.symm <| hi.1.eq_of_le hm.1.1 <| infₛ_le ⟨le_trans hij hjm, hm⟩
+  le_trans hjm <| le_of_eq <| Eq.symm <| hi.1.eq_of_le hm.1.1 <| sInf_le ⟨le_trans hij hjm, hm⟩
 #align ideal.is_local.le_jacobson Ideal.IsLocal.le_jacobson
 
 theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R) :
@@ -407,8 +407,8 @@ end IsLocal
 theorem isPrimary_of_isMaximal_radical [CommRing R] {I : Ideal R} (hi : IsMaximal (radical I)) :
     IsPrimary I :=
   have : radical I = jacobson I :=
-    le_antisymm (le_infₛ fun M ⟨him, hm⟩ => hm.IsPrime.radical_le_iff.2 him)
-      (infₛ_le ⟨le_radical, hi⟩)
+    le_antisymm (le_sInf fun M ⟨him, hm⟩ => hm.IsPrime.radical_le_iff.2 him)
+      (sInf_le ⟨le_radical, hi⟩)
   ⟨ne_top_of_lt <| lt_of_le_of_lt le_radical (lt_top_iff_ne_top.2 hi.1.1), fun x y hxy =>
     ((isLocal_of_isMaximal_radical hi).mem_jacobson_or_exists_inv y).symm.imp
       (fun ⟨z, hz⟩ => by

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -217,7 +217,7 @@ theorem map_jacobson_of_bijective {f : R →+* S} (hf : Function.Bijective f) :
 
 theorem comap_jacobson {f : R →+* S} {K : Ideal S} :
     comap f K.jacobson = infₛ (comap f '' { J : Ideal S | K ≤ J ∧ J.IsMaximal }) :=
-  trans (comap_Inf' f _) infₛ_eq_infᵢ.symm
+  trans (comap_infₛ' f _) infₛ_eq_infᵢ.symm
 #align ideal.comap_jacobson Ideal.comap_jacobson
 
 theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f) {K : Ideal S} :

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
 
 ! This file was ported from Lean 3 source module ring_theory.jacobson_ideal
-! leanprover-community/mathlib commit 79de90f7beca025f469dcda978ae655c4d985946
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Ideal.Quotient
-import Mathbin.RingTheory.Polynomial.Basic
+import Mathbin.RingTheory.Polynomial.Quotient
 
 /-!
 # Jacobson radical

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

@@ -337,7 +337,7 @@ open Polynomial
 variable [CommRing R]
 
 theorem jacobson_bot_polynomial_le_infₛ_map_maximal :
-    jacobson (⊥ : Ideal R[X]) ≤ infₛ (map (c : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
+    jacobson (⊥ : Ideal R[X]) ≤ infₛ (map (C : R →+* R[X]) '' { J : Ideal R | J.IsMaximal }) :=
   by
   refine' le_infₛ fun J => exists_imp.2 fun j hj => _
   haveI : j.is_maximal := hj.1

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

@@ -172,7 +172,7 @@ theorem eq_jacobson_iff_infₛ_maximal' :
           hM.2⟩⟩⟩
 #align ideal.eq_jacobson_iff_Inf_maximal' Ideal.eq_jacobson_iff_infₛ_maximal'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ∉ » I) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » I) -/
 /-- An ideal `I` equals its Jacobson radical if and only if every element outside `I`
 also lies outside of a maximal ideal containing `I`. -/
 theorem eq_jacobson_iff_not_mem :

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

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

@@ -3,6 +3,7 @@ Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
 -/
+import Mathlib.RingTheory.Ideal.IsPrimary
 import Mathlib.RingTheory.Ideal.Quotient
 import Mathlib.RingTheory.Polynomial.Quotient
 

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -104,11 +104,11 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
         let ⟨r, hr⟩ := mem_span_singleton'.1 hq
         ⟨r, by
           -- Porting note: supply `mul_add_one` with explicit variables
-          rw [mul_assoc, ← mul_add_one r (y * x), hr, ← hpq, ← neg_sub, add_sub_cancel]
+          rw [mul_assoc, ← mul_add_one r (y * x), hr, ← hpq, ← neg_sub, add_sub_cancel_right]
           exact I.neg_mem hpi⟩)
       fun hxy : I ⊔ span {y * x + 1} ≠ ⊤ => let ⟨M, hm1, hm2⟩ := exists_le_maximal _ hxy
       suffices x ∉ M from (this <| mem_sInf.1 hx ⟨le_trans le_sup_left hm2, hm1⟩).elim
-      fun hxm => hm1.1.1 <| (eq_top_iff_one _).2 <| add_sub_cancel' (y * x) 1 ▸
+      fun hxm => hm1.1.1 <| (eq_top_iff_one _).2 <| add_sub_cancel_left (y * x) 1 ▸
         M.sub_mem (le_sup_right.trans hm2 <| subset_span rfl) (M.mul_mem_left _ hxm),
     fun hx => mem_sInf.2 fun M ⟨him, hm⟩ => by_contradiction fun hxm =>
       let ⟨y, i, hi, df⟩ := hm.exists_inv hxm
@@ -386,7 +386,8 @@ theorem IsLocal.mem_jacobson_or_exists_inv {I : Ideal R} (hi : IsLocal I) (x : R
     (fun h : I ⊔ span {x} = ⊤ =>
       let ⟨p, hpi, q, hq, hpq⟩ := Submodule.mem_sup.1 ((eq_top_iff_one _).1 h)
       let ⟨r, hr⟩ := mem_span_singleton.1 hq
-      Or.inr ⟨r, by rw [← hpq, mul_comm, ← hr, ← neg_sub, add_sub_cancel]; exact I.neg_mem hpi⟩)
+      Or.inr ⟨r, by
+        rw [← hpq, mul_comm, ← hr, ← neg_sub, add_sub_cancel_right]; exact I.neg_mem hpi⟩)
     fun h : I ⊔ span {x} ≠ ⊤ =>
     Or.inl <|
       le_trans le_sup_right (hi.le_jacobson le_sup_left h) <| mem_span_singleton.2 <| dvd_refl x

Those lemmas have historically been very annoying to use in rw since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.

Downstream code broken by this change can fix it by adding appropriately many _s.

Also marks CauSeq.ext @[ext].

Order.BoundedOrder

• top_sup_eq
• sup_top_eq
• bot_sup_eq
• sup_bot_eq
• top_inf_eq
• inf_top_eq
• bot_inf_eq
• inf_bot_eq

Order.Lattice

• sup_idem
• sup_comm
• sup_assoc
• sup_left_idem
• sup_right_idem
• inf_idem
• inf_comm
• inf_assoc
• inf_left_idem
• inf_right_idem
• sup_inf_left
• sup_inf_right
• inf_sup_left
• inf_sup_right

Order.MinMax

• max_min_distrib_left
• max_min_distrib_right
• min_max_distrib_left
• min_max_distrib_right

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -210,19 +210,18 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
     comap f K.jacobson = (comap f K).jacobson := by
   unfold Ideal.jacobson
   refine' le_antisymm _ _
-  · refine le_trans (comap_mono (le_of_eq (Trans.trans top_inf_eq.symm sInf_insert.symm))) ?_
-    rw [comap_sInf', sInf_eq_iInf]
+  · rw [← top_inf_eq (sInf _), ← sInf_insert, comap_sInf', sInf_eq_iInf]
     refine' iInf_le_iInf_of_subset fun J hJ => _
     have : comap f (map f J) = J :=
       Trans.trans (comap_map_of_surjective f hf J)
         (le_antisymm (sup_le_iff.2 ⟨le_of_eq rfl, le_trans (comap_mono bot_le) hJ.left⟩)
           le_sup_left)
     cases' map_eq_top_or_isMaximal_of_surjective _ hf hJ.right with htop hmax
-    · exact ⟨⊤, ⟨Set.mem_insert ⊤ _, htop ▸ this⟩⟩
-    · exact ⟨map f J, ⟨Set.mem_insert_of_mem _ ⟨le_map_of_comap_le_of_surjective f hf hJ.1, hmax⟩,
-        this⟩⟩
-  · rw [comap_sInf]
-    refine' le_iInf_iff.2 fun J => le_iInf_iff.2 fun hJ => _
+    · exact ⟨⊤, Set.mem_insert ⊤ _, htop ▸ this⟩
+    · exact ⟨map f J, Set.mem_insert_of_mem _ ⟨le_map_of_comap_le_of_surjective f hf hJ.1, hmax⟩,
+        this⟩
+  · simp_rw [comap_sInf, le_iInf_iff]
+    intros J hJ
     haveI : J.IsMaximal := hJ.right
     exact sInf_le ⟨comap_mono hJ.left, comap_isMaximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -103,7 +103,7 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
         let ⟨p, hpi, q, hq, hpq⟩ := Submodule.mem_sup.1 ((eq_top_iff_one _).1 hxy)
         let ⟨r, hr⟩ := mem_span_singleton'.1 hq
         ⟨r, by
-          -- Porting note : supply `mul_add_one` with explicit variables
+          -- Porting note: supply `mul_add_one` with explicit variables
           rw [mul_assoc, ← mul_add_one r (y * x), hr, ← hpq, ← neg_sub, add_sub_cancel]
           exact I.neg_mem hpi⟩)
       fun hxy : I ⊔ span {y * x + 1} ≠ ⊤ => let ⟨M, hm1, hm2⟩ := exists_le_maximal _ hxy
@@ -115,7 +115,7 @@ theorem mem_jacobson_iff {x : R} : x ∈ jacobson I ↔ ∀ y, ∃ z, z * y * x
       let ⟨z, hz⟩ := hx (-y)
       hm.1.1 <| (eq_top_iff_one _).2 <| sub_sub_cancel (z * -y * x + z) 1 ▸
         M.sub_mem (by
-          -- Porting note : supply `mul_add_one` with explicit variables
+          -- Porting note: supply `mul_add_one` with explicit variables
           rw [mul_assoc, ← mul_add_one z, neg_mul, ← sub_eq_iff_eq_add.mpr df.symm, neg_sub,
             sub_add_cancel]
           exact M.mul_mem_left _ hi) <| him hz⟩
@@ -179,7 +179,7 @@ theorem map_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f)
     RingHom.ker f ≤ I → map f I.jacobson = (map f I).jacobson := by
   intro h
   unfold Ideal.jacobson
-  -- porting note : dot notation for `RingHom.ker` does not work
+  -- Porting note: dot notation for `RingHom.ker` does not work
   have : ∀ J ∈ { J : Ideal R | I ≤ J ∧ J.IsMaximal }, RingHom.ker f ≤ J :=
     fun J hJ => le_trans h hJ.left
   refine Trans.trans (map_sInf hf this) (le_antisymm ?_ ?_)
@@ -268,7 +268,7 @@ theorem mem_jacobson_bot {x : R} : x ∈ jacobson (⊥ : Ideal R) ↔ ∀ y, IsU
 
 /-- An ideal `I` of `R` is equal to its Jacobson radical if and only if
 the Jacobson radical of the quotient ring `R/I` is the zero ideal -/
--- Porting note : changed `Quotient.mk'` to ``
+-- Porting note: changed `Quotient.mk'` to ``
 theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
     I.jacobson = I ↔ jacobson (⊥ : Ideal (R ⧸ I)) = ⊥ := by
   have hf : Function.Surjective (Ideal.Quotient.mk I) := Submodule.Quotient.mk_surjective I
@@ -285,7 +285,7 @@ theorem jacobson_eq_iff_jacobson_quotient_eq_bot :
 
 /-- The standard radical and Jacobson radical of an ideal `I` of `R` are equal if and only if
 the nilradical and Jacobson radical of the quotient ring `R/I` coincide -/
--- Porting note : changed `Quotient.mk'` to ``
+-- Porting note: changed `Quotient.mk'` to ``
 theorem radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot :
     I.radical = I.jacobson ↔ radical (⊥ : Ideal (R ⧸ I)) = jacobson ⊥ := by
   have hf : Function.Surjective (Ideal.Quotient.mk I) := Submodule.Quotient.mk_surjective I

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.

@@ -224,7 +224,7 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
   · rw [comap_sInf]
     refine' le_iInf_iff.2 fun J => le_iInf_iff.2 fun hJ => _
     haveI : J.IsMaximal := hJ.right
-    refine' sInf_le ⟨comap_mono hJ.left, comap_isMaximal_of_surjective _ hf⟩
+    exact sInf_le ⟨comap_mono hJ.left, comap_isMaximal_of_surjective _ hf⟩
 #align ideal.comap_jacobson_of_surjective Ideal.comap_jacobson_of_surjective
 
 @[mono]

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.jacobson_ideal
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Ideal.Quotient
 import Mathlib.RingTheory.Polynomial.Quotient
 
+#align_import ring_theory.jacobson_ideal from "leanprover-community/mathlib"@"da420a8c6dd5bdfb85c4ced85c34388f633bc6ff"
+
 /-!
 # Jacobson radical
 

Changes are of the form

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

@@ -169,7 +169,7 @@ theorem eq_jacobson_iff_not_mem :
   constructor
   · intro h x hx
     erw [← h, mem_sInf] at hx
-    push_neg  at hx
+    push_neg at hx
     exact hx
   · refine fun h => le_antisymm (fun x hx => ?_) le_jacobson
     contrapose hx
@@ -233,7 +233,7 @@ theorem comap_jacobson_of_surjective {f : R →+* S} (hf : Function.Surjective f
 @[mono]
 theorem jacobson_mono {I J : Ideal R} : I ≤ J → I.jacobson ≤ J.jacobson := by
   intro h x hx
-  erw [mem_sInf] at hx⊢
+  erw [mem_sInf] at hx ⊢
   exact fun K ⟨hK, hK_max⟩ => hx ⟨Trans.trans h hK, hK_max⟩
 #align ideal.jacobson_mono Ideal.jacobson_mono
 

These are all doc fixes

@@ -341,7 +341,7 @@ theorem jacobson_bot_polynomial_le_sInf_map_maximal :
   simp only [coeff_add, mul_coeff_zero, coeff_X_zero, mul_zero, coeff_one_zero, zero_add] at r2
   erw [add_left_eq_self] at r2
   simpa using (mul_eq_zero.mp r2).resolve_right r1
-  -- Poring note: this is golfed to much
+  -- Porting note: this is golfed to much
   -- simpa [(fun hX => by simpa using congr_arg (fun f => coeff f 1) hX : (X : (R ⧸ j)[X]) ≠ 0)]
   --   using eq_C_of_degree_eq_zero (degree_eq_zero_of_is_unit ((mem_jacobson_bot.1 hf) X))
 #align ideal.jacobson_bot_polynomial_le_Inf_map_maximal Ideal.jacobson_bot_polynomial_le_sInf_map_maximal

@@ -27,15 +27,16 @@ as the intersection of maximal ideals containing `I`.
 
 Let `R` be a commutative ring, and `I` be an ideal of `R`
 
-* `jacobson I` is the jacobson radical, i.e. the infimum of all maximal ideals containing I.
+* `Ideal.jacobson I` is the jacobson radical, i.e. the infimum of all maximal ideals containing I.
 
-* `is_local I` is the proposition that the jacobson radical of `I` is itself a maximal ideal
+* `Ideal.IsLocal I` is the proposition that the jacobson radical of `I` is itself a maximal ideal
 
 ## Main statements
 
 * `mem_jacobson_iff` gives a characterization of members of the jacobson of I
 
-* `is_local_of_is_maximal_radical`: if the radical of I is maximal then so is the jacobson radical
+* `Ideal.isLocal_of_isMaximal_radical`: if the radical of I is maximal then so is the jacobson
+  radical
 
 ## Tags