ring_theory.ideal.over | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

198cb64d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61db041a

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -48,7 +48,7 @@ variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f :=
   by
-  rw [← p.div_X_mul_X_add, eval₂_add, eval₂_C, eval₂_mul, eval₂_X] at hp 
+  rw [← p.div_X_mul_X_add, eval₂_add, eval₂_C, eval₂_mul, eval₂_X] at hp
   refine' mem_comap.mpr ((I.add_mem_iff_right _).mp hp)
   exact I.mul_mem_left _ hr
 #align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem
@@ -72,7 +72,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     refine' ⟨0, _, coeff_zero_mem_comap_of_root_mem hr hp⟩
     simp [coeff_eq_zero, a_ne_zero]
   · intro p p_nonzero ih mul_nonzero hp
-    rw [eval₂_mul, eval₂_X] at hp 
+    rw [eval₂_mul, eval₂_X] at hp
     obtain ⟨i, hi, mem⟩ := ih p_nonzero (r_non_zero_divisor hp)
     refine' ⟨i + 1, _, _⟩ <;> simp [hi, mem]
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
@@ -247,7 +247,7 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
     exact trans (eval₂_map _ _ _) (hom_eval₂ p f (Quotient.mk' I) r).symm
   obtain ⟨i, ne_zero, mem⟩ :=
     exists_coeff_ne_zero_mem_comap_of_root_mem rbar_ne_zero rbar_mem_J p_ne_zero rbar_root
-  rw [coeff_map] at ne_zero mem 
+  rw [coeff_map] at ne_zero mem
   refine' ⟨i, (mem_quotient_iff_mem hIJ).mp _, mt _ NeZero⟩
   · simpa using mem
   simp [quotient.eq_zero_iff_mem]

61db041a

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -345,7 +345,7 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
   refine' quotient.maximal_of_is_field _ _
   haveI : is_prime (I.comap (algebraMap R S)) := comap_is_prime _ _
   exact
-    isField_of_isIntegral_of_isField (isIntegral_quotient_of_isIntegral hRS)
+    isField_of_isIntegral_of_isField (Algebra.IsIntegral.quotient hRS)
       algebra_map_quotient_injective (by rwa [← quotient.maximal_ideal_iff_is_field_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 -/
@@ -430,10 +430,10 @@ theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integr
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
 -/
 
-#print Ideal.exists_ideal_over_prime_of_isIntegral' /-
+#print Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomain /-
 /-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
-theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P : Ideal R)
+theorem exists_ideal_over_prime_of_isIntegral_of_isDomain (H : Algebra.IsIntegral R S) (P : Ideal R)
     [IsPrime P] (hP : (algebraMap R S).ker ≤ P) :
     ∃ Q : Ideal S, IsPrime Q ∧ Q.comap (algebraMap R S) = P :=
   by
@@ -453,7 +453,7 @@ theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P :
   convert Localization.AtPrime.comap_maximalIdeal
   rw [comap_comap, ← LocalRing.eq_maximalIdeal Qₚ_max, ← IsLocalization.map_comp _]
   rfl
-#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral'
+#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomain
 -/
 
 end
@@ -469,7 +469,7 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
   let quot := R ⧸ I.comap (algebraMap R S)
   obtain ⟨Q' : Ideal (S ⧸ I), ⟨Q'_prime, hQ'⟩⟩ :=
     @exists_ideal_over_prime_of_is_integral' Quot _ (S ⧸ I) _ Ideal.quotientAlgebra _
-      (isIntegral_quotient_of_isIntegral H) (map (Quotient.mk' (I.comap (algebraMap R S))) P)
+      (Algebra.IsIntegral.quotient H) (map (Quotient.mk' (I.comap (algebraMap R S))) P)
       (map_is_prime_of_surjective quotient.mk_surjective (by simp [hIP]))
       (le_trans (le_of_eq ((RingHom.injective_iff_ker_eq_bot _).1 algebra_map_quotient_injective))
         bot_le)

61db041a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.RingTheory.Algebraic
-import Mathbin.RingTheory.Localization.AtPrime
-import Mathbin.RingTheory.Localization.Integral
+import RingTheory.Algebraic
+import RingTheory.Localization.AtPrime
+import RingTheory.Localization.Integral
 
 #align_import ring_theory.ideal.over from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"

61db041a

bump to nightly-2023-09-10-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

783dcb10

Diff

@@ -165,11 +165,11 @@ theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S 
 #align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotient
 -/
 
-#print Ideal.Quotient.algebraQuotientOfLeComap /-
+#print Ideal.Quotient.algebraQuotientOfLEComap /-
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`. -/
-def Quotient.algebraQuotientOfLeComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
+def Quotient.algebraQuotientOfLEComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
   RingHom.toAlgebra <| quotientMap _ f h
-#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComap
+#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLEComap
 -/
 
 #print Ideal.Quotient.algebraQuotientMapQuotient /-

61db041a

bump to nightly-2023-08-31-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ffde2d8a6e689149e44fd95fa862c23a57f8c780

8d006b5f

Diff

@@ -430,10 +430,10 @@ theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integr
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
 -/
 
-#print Ideal.exists_ideal_over_prime_of_is_integral' /-
+#print Ideal.exists_ideal_over_prime_of_isIntegral' /-
 /-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
-theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
+theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P : Ideal R)
     [IsPrime P] (hP : (algebraMap R S).ker ≤ P) :
     ∃ Q : Ideal S, IsPrime Q ∧ Q.comap (algebraMap R S) = P :=
   by
@@ -453,7 +453,7 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
   convert Localization.AtPrime.comap_maximalIdeal
   rw [comap_comap, ← LocalRing.eq_maximalIdeal Qₚ_max, ← IsLocalization.map_comp _]
   rfl
-#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_is_integral'
+#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral'
 -/
 
 end

61db041a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.ideal.over
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Algebraic
 import Mathbin.RingTheory.Localization.AtPrime
 import Mathbin.RingTheory.Localization.Integral
 
+#align_import ring_theory.ideal.over from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Ideals over/under ideals

61db041a

bump to nightly-2023-07-04-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

8a4e8caf

Diff

@@ -353,11 +353,11 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 -/
 
-#print Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' /-
-theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
+#print Ideal.isMaximal_comap_of_isIntegral_of_isMaximal' /-
+theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type _} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
-#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'
+#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_isMaximal'
 -/
 
 section IsIntegralClosure

61db041a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,6 +47,7 @@ section CommRing
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
+#print Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem /-
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f :=
   by
@@ -54,12 +55,16 @@ theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p :
   refine' mem_comap.mpr ((I.add_mem_iff_right _).mp hp)
   exact I.mul_mem_left _ hr
 #align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem
+-/
 
+#print Ideal.coeff_zero_mem_comap_of_root_mem /-
 theorem coeff_zero_mem_comap_of_root_mem {r : S} (hr : r ∈ I) {p : R[X]} (hp : p.eval₂ f r = 0) :
     p.coeff 0 ∈ I.comap f :=
   coeff_zero_mem_comap_of_root_mem_of_eval_mem hr (hp.symm ▸ I.zero_mem)
 #align ideal.coeff_zero_mem_comap_of_root_mem Ideal.coeff_zero_mem_comap_of_root_mem
+-/
 
+#print Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem /-
 theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     (r_non_zero_divisor : ∀ {x}, x * r = 0 → x = 0) (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
@@ -74,6 +79,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     obtain ⟨i, hi, mem⟩ := ih p_nonzero (r_non_zero_divisor hp)
     refine' ⟨i + 1, _, _⟩ <;> simp [hi, mem]
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
+-/
 
 #print Ideal.injective_quotient_le_comap_map /-
 /-- Let `P` be an ideal in `R[x]`.  The map
@@ -118,6 +124,7 @@ theorem quotient_mk_maps_eq (P : Ideal R[X]) :
 #align ideal.quotient_mk_maps_eq Ideal.quotient_mk_maps_eq
 -/
 
+#print Ideal.exists_nonzero_mem_of_ne_bot /-
 /-- This technical lemma asserts the existence of a polynomial `p` in an ideal `P ⊂ R[x]`
 that is non-zero in the quotient `R / (P ∩ R) [x]`.  The assumptions are equivalent to
 `P ≠ 0` and `P ∩ R = (0)`.
@@ -134,9 +141,11 @@ theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀
   rw [mk_ker]
   exact (Submodule.eq_bot_iff _).mpr fun x hx => hP x (mem_comap.mp hx)
 #align ideal.exists_nonzero_mem_of_ne_bot Ideal.exists_nonzero_mem_of_ne_bot
+-/
 
 variable {p : Ideal R} {P : Ideal S}
 
+#print Ideal.comap_eq_of_scalar_tower_quotient /-
 /-- If there is an injective map `R/p → S/P` such that following diagram commutes:
 ```
 R   → S
@@ -157,11 +166,14 @@ theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S 
   · intro hx
     rw [hx, RingHom.map_zero]
 #align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotient
+-/
 
+#print Ideal.Quotient.algebraQuotientOfLeComap /-
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`. -/
 def Quotient.algebraQuotientOfLeComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
   RingHom.toAlgebra <| quotientMap _ f h
 #align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComap
+-/
 
 #print Ideal.Quotient.algebraQuotientMapQuotient /-
 /-- `R / p` has a canonical map to `S / pS`. -/
@@ -210,13 +222,16 @@ section IsDomain
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
+#print Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem /-
 theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0)
     (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
   exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
     (fun _ h => Or.resolve_right (mul_eq_zero.mp h) r_ne_zero) hr
 #align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem
+-/
 
+#print Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff /-
 theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hpI : p.eval₂ f r ∈ I) : ∃ i, p.coeff i ∈ (J.comap f : Set R) \ I.comap f :=
@@ -240,18 +255,24 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
   · simpa using mem
   simp [quotient.eq_zero_iff_mem]
 #align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff
+-/
 
+#print Ideal.comap_lt_comap_of_root_mem_sdiff /-
 theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hp : p.eval₂ f r ∈ I) : I.comap f < J.comap f :=
   let ⟨i, hJ, hI⟩ := exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff hIJ hr p_ne_zero hp
   SetLike.lt_iff_le_and_exists.mpr ⟨comap_mono hIJ, p.coeff i, hJ, hI⟩
 #align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiff
+-/
 
+#print Ideal.mem_of_one_mem /-
 theorem mem_of_one_mem (h : (1 : S) ∈ I) (x) : x ∈ I :=
   (I.eq_top_iff_one.mpr h).symm ▸ mem_top
 #align ideal.mem_of_one_mem Ideal.mem_of_one_mem
+-/
 
+#print Ideal.comap_lt_comap_of_integral_mem_sdiff /-
 theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ : I ≤ J) {x : S}
     (mem : x ∈ (J : Set S) \ I) (integral : IsIntegral R x) :
     I.comap (algebraMap R S) < J.comap (algebraMap R S) :=
@@ -265,13 +286,17 @@ theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ
     apply hI.1
   convert I.zero_mem
 #align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiff
+-/
 
+#print Ideal.comap_ne_bot_of_root_mem /-
 theorem comap_ne_bot_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0) (hr : r ∈ I) {p : R[X]}
     (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0) : I.comap f ≠ ⊥ := fun h =>
   let ⟨i, hi, mem⟩ := exists_coeff_ne_zero_mem_comap_of_root_mem r_ne_zero hr p_ne_zero hp
   absurd (mem_bot.mp (eq_bot_iff.mp h mem)) hi
 #align ideal.comap_ne_bot_of_root_mem Ideal.comap_ne_bot_of_root_mem
+-/
 
+#print Ideal.isMaximal_of_isIntegral_of_isMaximal_comap /-
 theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.IsIntegral R S)
     (I : Ideal S) [I.IsPrime] (hI : IsMaximal (I.comap (algebraMap R S))) : IsMaximal I :=
   ⟨⟨mt comap_eq_top_iff.mpr hI.1.1, fun J I_lt_J =>
@@ -279,25 +304,33 @@ theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.
       comap_eq_top_iff.1 <|
         hI.1.2 _ (comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (hRS x))⟩⟩
 #align ideal.is_maximal_of_is_integral_of_is_maximal_comap Ideal.isMaximal_of_isIntegral_of_isMaximal_comap
+-/
 
+#print Ideal.isMaximal_of_isIntegral_of_isMaximal_comap' /-
 theorem isMaximal_of_isIntegral_of_isMaximal_comap' (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S)
     [hI' : I.IsPrime] (hI : IsMaximal (I.comap f)) : IsMaximal I :=
   @isMaximal_of_isIntegral_of_isMaximal_comap R _ S _ f.toAlgebra hf I hI' hI
 #align ideal.is_maximal_of_is_integral_of_is_maximal_comap' Ideal.isMaximal_of_isIntegral_of_isMaximal_comap'
+-/
 
 variable [Algebra R S]
 
+#print Ideal.comap_ne_bot_of_algebraic_mem /-
 theorem comap_ne_bot_of_algebraic_mem [IsDomain S] {x : S} (x_ne_zero : x ≠ 0) (x_mem : x ∈ I)
     (hx : IsAlgebraic R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   let ⟨p, p_ne_zero, hp⟩ := hx
   comap_ne_bot_of_root_mem x_ne_zero x_mem p_ne_zero hp
 #align ideal.comap_ne_bot_of_algebraic_mem Ideal.comap_ne_bot_of_algebraic_mem
+-/
 
+#print Ideal.comap_ne_bot_of_integral_mem /-
 theorem comap_ne_bot_of_integral_mem [Nontrivial R] [IsDomain S] {x : S} (x_ne_zero : x ≠ 0)
     (x_mem : x ∈ I) (hx : IsIntegral R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   comap_ne_bot_of_algebraic_mem x_ne_zero x_mem (hx.IsAlgebraic R)
 #align ideal.comap_ne_bot_of_integral_mem Ideal.comap_ne_bot_of_integral_mem
+-/
 
+#print Ideal.eq_bot_of_comap_eq_bot /-
 theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsIntegral R S)
     (hI : I.comap (algebraMap R S) = ⊥) : I = ⊥ :=
   by
@@ -306,7 +339,9 @@ theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsInte
   · exact hx0.symm ▸ Ideal.zero_mem ⊥
   · exact absurd hI (comap_ne_bot_of_integral_mem hx0 hx (hRS x))
 #align ideal.eq_bot_of_comap_eq_bot Ideal.eq_bot_of_comap_eq_bot
+-/
 
+#print Ideal.isMaximal_comap_of_isIntegral_of_isMaximal /-
 theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S) (I : Ideal S)
     [hI : I.IsMaximal] : IsMaximal (I.comap (algebraMap R S)) :=
   by
@@ -316,11 +351,14 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
     isField_of_isIntegral_of_isField (isIntegral_quotient_of_isIntegral hRS)
       algebra_map_quotient_injective (by rwa [← quotient.maximal_ideal_iff_is_field_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
+-/
 
+#print Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' /-
 theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'
+-/
 
 section IsIntegralClosure
 
@@ -328,57 +366,74 @@ variable (S) {A : Type _} [CommRing A]
 
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]
 
+#print Ideal.IsIntegralClosure.comap_lt_comap /-
 theorem IsIntegralClosure.comap_lt_comap {I J : Ideal A} [I.IsPrime] (I_lt_J : I < J) :
     I.comap (algebraMap R A) < J.comap (algebraMap R A) :=
   let ⟨I_le_J, x, hxJ, hxI⟩ := SetLike.lt_iff_le_and_exists.mp I_lt_J
   comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comap
+-/
 
+#print Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comap /-
 theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R A))) : IsMaximal I :=
   isMaximal_of_isIntegral_of_isMaximal_comap (fun x => IsIntegralClosure.isIntegral R S x) I hI
 #align ideal.is_integral_closure.is_maximal_of_is_maximal_comap Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comap
+-/
 
 variable [IsDomain A]
 
+#print Ideal.IsIntegralClosure.comap_ne_bot /-
 theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot : I ≠ ⊥) :
     I.comap (algebraMap R A) ≠ ⊥ :=
   let ⟨x, x_mem, x_ne_zero⟩ := I.ne_bot_iff.mp I_ne_bot
   comap_ne_bot_of_integral_mem x_ne_zero x_mem (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_bot
+-/
 
+#print Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot /-
 theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
     I.comap (algebraMap R A) = ⊥ → I = ⊥ :=
   imp_of_not_imp_not _ _ (IsIntegralClosure.comap_ne_bot S)
 #align ideal.is_integral_closure.eq_bot_of_comap_eq_bot Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot
+-/
 
 end IsIntegralClosure
 
+#print Ideal.IntegralClosure.comap_lt_comap /-
 theorem IntegralClosure.comap_lt_comap {I J : Ideal (integralClosure R S)} [I.IsPrime]
     (I_lt_J : I < J) :
     I.comap (algebraMap R (integralClosure R S)) < J.comap (algebraMap R (integralClosure R S)) :=
   IsIntegralClosure.comap_lt_comap S I_lt_J
 #align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comap
+-/
 
+#print Ideal.IntegralClosure.isMaximal_of_isMaximal_comap /-
 theorem IntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal (integralClosure R S)) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R (integralClosure R S)))) : IsMaximal I :=
   IsIntegralClosure.isMaximal_of_isMaximal_comap S I hI
 #align ideal.integral_closure.is_maximal_of_is_maximal_comap Ideal.IntegralClosure.isMaximal_of_isMaximal_comap
+-/
 
 section
 
 variable [IsDomain S]
 
+#print Ideal.IntegralClosure.comap_ne_bot /-
 theorem IntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal (integralClosure R S)}
     (I_ne_bot : I ≠ ⊥) : I.comap (algebraMap R (integralClosure R S)) ≠ ⊥ :=
   IsIntegralClosure.comap_ne_bot S I_ne_bot
 #align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_bot
+-/
 
+#print Ideal.IntegralClosure.eq_bot_of_comap_eq_bot /-
 theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integralClosure R S)} :
     I.comap (algebraMap R (integralClosure R S)) = ⊥ → I = ⊥ :=
   IsIntegralClosure.eq_bot_of_comap_eq_bot S
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
+-/
 
+#print Ideal.exists_ideal_over_prime_of_is_integral' /-
 /-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
@@ -402,9 +457,11 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
   rw [comap_comap, ← LocalRing.eq_maximalIdeal Qₚ_max, ← IsLocalization.map_comp _]
   rfl
 #align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_is_integral'
+-/
 
 end
 
+#print Ideal.exists_ideal_over_prime_of_isIntegral /-
 /-- More general going-up theorem than `exists_ideal_over_prime_of_is_integral'`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?
   Not sure how best to write an ascending chain in Lean -/
@@ -427,7 +484,9 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
   · refine' trans (comap_map_of_surjective _ quotient.mk_surjective _) (sup_eq_left.2 _)
     simpa [← RingHom.ker_eq_comap_bot] using hIP
 #align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegral
+-/
 
+#print Ideal.exists_ideal_over_maximal_of_isIntegral /-
 /-- `comap (algebra_map R S)` is a surjection from the max spec of `S` to max spec of `R`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)
@@ -438,6 +497,7 @@ theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsInte
   haveI : Q.is_prime := Q_prime
   exact ⟨Q, is_maximal_of_is_integral_of_is_maximal_comap H _ (hQ.symm ▸ P_max), hQ⟩
 #align ideal.exists_ideal_over_maximal_of_is_integral Ideal.exists_ideal_over_maximal_of_isIntegral
+-/
 
 end IsDomain

61db041a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -50,7 +50,7 @@ variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f :=
   by
-  rw [← p.div_X_mul_X_add, eval₂_add, eval₂_C, eval₂_mul, eval₂_X] at hp
+  rw [← p.div_X_mul_X_add, eval₂_add, eval₂_C, eval₂_mul, eval₂_X] at hp 
   refine' mem_comap.mpr ((I.add_mem_iff_right _).mp hp)
   exact I.mul_mem_left _ hr
 #align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem
@@ -70,7 +70,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     refine' ⟨0, _, coeff_zero_mem_comap_of_root_mem hr hp⟩
     simp [coeff_eq_zero, a_ne_zero]
   · intro p p_nonzero ih mul_nonzero hp
-    rw [eval₂_mul, eval₂_X] at hp
+    rw [eval₂_mul, eval₂_X] at hp 
     obtain ⟨i, hi, mem⟩ := ih p_nonzero (r_non_zero_divisor hp)
     refine' ⟨i + 1, _, _⟩ <;> simp [hi, mem]
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
@@ -235,7 +235,7 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
     exact trans (eval₂_map _ _ _) (hom_eval₂ p f (Quotient.mk' I) r).symm
   obtain ⟨i, ne_zero, mem⟩ :=
     exists_coeff_ne_zero_mem_comap_of_root_mem rbar_ne_zero rbar_mem_J p_ne_zero rbar_root
-  rw [coeff_map] at ne_zero mem
+  rw [coeff_map] at ne_zero mem 
   refine' ⟨i, (mem_quotient_iff_mem hIJ).mp _, mt _ NeZero⟩
   · simpa using mem
   simp [quotient.eq_zero_iff_mem]

61db041a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -39,7 +39,7 @@ namespace Ideal
 
 open Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 open Submodule

61db041a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -47,12 +47,6 @@ section CommRing
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
-/- warning: ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem -> Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {r : S}, (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (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))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {r : S}, (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (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))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))
-Case conversion may be inaccurate. Consider using '#align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_memₓ'. -/
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f :=
   by
@@ -61,23 +55,11 @@ theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p :
   exact I.mul_mem_left _ hr
 #align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem
 
-/- warning: ideal.coeff_zero_mem_comap_of_root_mem -> Ideal.coeff_zero_mem_comap_of_root_mem is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align ideal.coeff_zero_mem_comap_of_root_mem Ideal.coeff_zero_mem_comap_of_root_memₓ'. -/
 theorem coeff_zero_mem_comap_of_root_mem {r : S} (hr : r ∈ I) {p : R[X]} (hp : p.eval₂ f r = 0) :
     p.coeff 0 ∈ I.comap f :=
   coeff_zero_mem_comap_of_root_mem_of_eval_mem hr (hp.symm ▸ I.zero_mem)
 #align ideal.coeff_zero_mem_comap_of_root_mem Ideal.coeff_zero_mem_comap_of_root_mem
 
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_memₓ'. -/
 theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     (r_non_zero_divisor : ∀ {x}, x * r = 0 → x = 0) (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
@@ -136,9 +118,6 @@ theorem quotient_mk_maps_eq (P : Ideal R[X]) :
 #align ideal.quotient_mk_maps_eq Ideal.quotient_mk_maps_eq
 -/
 
-/- warning: ideal.exists_nonzero_mem_of_ne_bot -> Ideal.exists_nonzero_mem_of_ne_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.exists_nonzero_mem_of_ne_bot Ideal.exists_nonzero_mem_of_ne_botₓ'. -/
 /-- This technical lemma asserts the existence of a polynomial `p` in an ideal `P ⊂ R[x]`
 that is non-zero in the quotient `R / (P ∩ R) [x]`.  The assumptions are equivalent to
 `P ≠ 0` and `P ∩ R = (0)`.
@@ -158,9 +137,6 @@ theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀
 
 variable {p : Ideal R} {P : Ideal S}
 
-/- warning: ideal.comap_eq_of_scalar_tower_quotient -> Ideal.comap_eq_of_scalar_tower_quotient is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotientₓ'. -/
 /-- If there is an injective map `R/p → S/P` such that following diagram commutes:
 ```
 R   → S
@@ -182,12 +158,6 @@ theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S 
     rw [hx, RingHom.map_zero]
 #align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotient
 
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-Case conversion may be inaccurate. Consider using '#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComapₓ'. -/
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`. -/
 def Quotient.algebraQuotientOfLeComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
   RingHom.toAlgebra <| quotientMap _ f h
@@ -240,12 +210,6 @@ section IsDomain
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
-/- warning: ideal.exists_coeff_ne_zero_mem_comap_of_root_mem -> Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_memₓ'. -/
 theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0)
     (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
@@ -253,9 +217,6 @@ theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_ze
     (fun _ h => Or.resolve_right (mul_eq_zero.mp h) r_ne_zero) hr
 #align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem
 
-/- warning: ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff -> Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiffₓ'. -/
 theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hpI : p.eval₂ f r ∈ I) : ∃ i, p.coeff i ∈ (J.comap f : Set R) \ I.comap f :=
@@ -280,9 +241,6 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
   simp [quotient.eq_zero_iff_mem]
 #align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff
 
-/- warning: ideal.comap_lt_comap_of_root_mem_sdiff -> Ideal.comap_lt_comap_of_root_mem_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hp : p.eval₂ f r ∈ I) : I.comap f < J.comap f :=
@@ -290,19 +248,10 @@ theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
   SetLike.lt_iff_le_and_exists.mpr ⟨comap_mono hIJ, p.coeff i, hJ, hI⟩
 #align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiff
 
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_of_one_mem Ideal.mem_of_one_memₓ'. -/
 theorem mem_of_one_mem (h : (1 : S) ∈ I) (x) : x ∈ I :=
   (I.eq_top_iff_one.mpr h).symm ▸ mem_top
 #align ideal.mem_of_one_mem Ideal.mem_of_one_mem
 
-/- warning: ideal.comap_lt_comap_of_integral_mem_sdiff -> Ideal.comap_lt_comap_of_integral_mem_sdiff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ : I ≤ J) {x : S}
     (mem : x ∈ (J : Set S) \ I) (integral : IsIntegral R x) :
     I.comap (algebraMap R S) < J.comap (algebraMap R S) :=
@@ -317,24 +266,12 @@ theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ
   convert I.zero_mem
 #align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiff
 
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 theorem comap_ne_bot_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0) (hr : r ∈ I) {p : R[X]}
     (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0) : I.comap f ≠ ⊥ := fun h =>
   let ⟨i, hi, mem⟩ := exists_coeff_ne_zero_mem_comap_of_root_mem r_ne_zero hr p_ne_zero hp
   absurd (mem_bot.mp (eq_bot_iff.mp h mem)) hi
 #align ideal.comap_ne_bot_of_root_mem Ideal.comap_ne_bot_of_root_mem
 
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-Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_of_is_integral_of_is_maximal_comap Ideal.isMaximal_of_isIntegral_of_isMaximal_comapₓ'. -/
 theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.IsIntegral R S)
     (I : Ideal S) [I.IsPrime] (hI : IsMaximal (I.comap (algebraMap R S))) : IsMaximal I :=
   ⟨⟨mt comap_eq_top_iff.mpr hI.1.1, fun J I_lt_J =>
@@ -343,12 +280,6 @@ theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.
         hI.1.2 _ (comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (hRS x))⟩⟩
 #align ideal.is_maximal_of_is_integral_of_is_maximal_comap Ideal.isMaximal_of_isIntegral_of_isMaximal_comap
 
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 theorem isMaximal_of_isIntegral_of_isMaximal_comap' (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S)
     [hI' : I.IsPrime] (hI : IsMaximal (I.comap f)) : IsMaximal I :=
   @isMaximal_of_isIntegral_of_isMaximal_comap R _ S _ f.toAlgebra hf I hI' hI
@@ -356,35 +287,17 @@ theorem isMaximal_of_isIntegral_of_isMaximal_comap' (f : R →+* S) (hf : f.IsIn
 
 variable [Algebra R S]
 
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 theorem comap_ne_bot_of_algebraic_mem [IsDomain S] {x : S} (x_ne_zero : x ≠ 0) (x_mem : x ∈ I)
     (hx : IsAlgebraic R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   let ⟨p, p_ne_zero, hp⟩ := hx
   comap_ne_bot_of_root_mem x_ne_zero x_mem p_ne_zero hp
 #align ideal.comap_ne_bot_of_algebraic_mem Ideal.comap_ne_bot_of_algebraic_mem
 
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 theorem comap_ne_bot_of_integral_mem [Nontrivial R] [IsDomain S] {x : S} (x_ne_zero : x ≠ 0)
     (x_mem : x ∈ I) (hx : IsIntegral R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   comap_ne_bot_of_algebraic_mem x_ne_zero x_mem (hx.IsAlgebraic R)
 #align ideal.comap_ne_bot_of_integral_mem Ideal.comap_ne_bot_of_integral_mem
 
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-Case conversion may be inaccurate. Consider using '#align ideal.eq_bot_of_comap_eq_bot Ideal.eq_bot_of_comap_eq_botₓ'. -/
 theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsIntegral R S)
     (hI : I.comap (algebraMap R S) = ⊥) : I = ⊥ :=
   by
@@ -394,12 +307,6 @@ theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsInte
   · exact absurd hI (comap_ne_bot_of_integral_mem hx0 hx (hRS x))
 #align ideal.eq_bot_of_comap_eq_bot Ideal.eq_bot_of_comap_eq_bot
 
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-Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximalₓ'. -/
 theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S) (I : Ideal S)
     [hI : I.IsMaximal] : IsMaximal (I.comap (algebraMap R S)) :=
   by
@@ -410,12 +317,6 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
       algebra_map_quotient_injective (by rwa [← quotient.maximal_ideal_iff_is_field_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
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-Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'ₓ'. -/
 theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
@@ -427,21 +328,12 @@ variable (S) {A : Type _} [CommRing A]
 
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]
 
-/- warning: ideal.is_integral_closure.comap_lt_comap -> Ideal.IsIntegralClosure.comap_lt_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comapₓ'. -/
 theorem IsIntegralClosure.comap_lt_comap {I J : Ideal A} [I.IsPrime] (I_lt_J : I < J) :
     I.comap (algebraMap R A) < J.comap (algebraMap R A) :=
   let ⟨I_le_J, x, hxJ, hxI⟩ := SetLike.lt_iff_le_and_exists.mp I_lt_J
   comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comap
 
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(MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] (I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) [_inst_9 : Ideal.IsPrime.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I)) -> (Ideal.IsMaximal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u2}} [_inst_4 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))] [_inst_6 : Algebra.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u2, u3} R A S (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) (Algebra.toSMul.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u2, u1, u3} A R S _inst_1 (CommRing.toCommSemiring.{u2} A _inst_4) _inst_2 _inst_3 _inst_6] (I : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) [_inst_9 : Ideal.IsPrime.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) I)) -> (Ideal.IsMaximal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I)
-Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.is_maximal_of_is_maximal_comap Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comapₓ'. -/
 theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R A))) : IsMaximal I :=
   isMaximal_of_isIntegral_of_isMaximal_comap (fun x => IsIntegralClosure.isIntegral R S x) I hI
@@ -449,18 +341,12 @@ theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
 
 variable [IsDomain A]
 
-/- warning: ideal.is_integral_closure.comap_ne_bot -> Ideal.IsIntegralClosure.comap_ne_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_botₓ'. -/
 theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot : I ≠ ⊥) :
     I.comap (algebraMap R A) ≠ ⊥ :=
   let ⟨x, x_mem, x_ne_zero⟩ := I.ne_bot_iff.mp I_ne_bot
   comap_ne_bot_of_integral_mem x_ne_zero x_mem (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_bot
 
-/- warning: ideal.is_integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.eq_bot_of_comap_eq_bot Ideal.IsIntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
     I.comap (algebraMap R A) = ⊥ → I = ⊥ :=
   imp_of_not_imp_not _ _ (IsIntegralClosure.comap_ne_bot S)
@@ -468,18 +354,12 @@ theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
 
 end IsIntegralClosure
 
-/- warning: ideal.integral_closure.comap_lt_comap -> Ideal.IntegralClosure.comap_lt_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comapₓ'. -/
 theorem IntegralClosure.comap_lt_comap {I J : Ideal (integralClosure R S)} [I.IsPrime]
     (I_lt_J : I < J) :
     I.comap (algebraMap R (integralClosure R S)) < J.comap (algebraMap R (integralClosure R S)) :=
   IsIntegralClosure.comap_lt_comap S I_lt_J
 #align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comap
 
-/- warning: ideal.integral_closure.is_maximal_of_is_maximal_comap -> Ideal.IntegralClosure.isMaximal_of_isMaximal_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.is_maximal_of_is_maximal_comap Ideal.IntegralClosure.isMaximal_of_isMaximal_comapₓ'. -/
 theorem IntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal (integralClosure R S)) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R (integralClosure R S)))) : IsMaximal I :=
   IsIntegralClosure.isMaximal_of_isMaximal_comap S I hI
@@ -489,28 +369,16 @@ section
 
 variable [IsDomain S]
 
-/- warning: ideal.integral_closure.comap_ne_bot -> Ideal.IntegralClosure.comap_ne_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_botₓ'. -/
 theorem IntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal (integralClosure R S)}
     (I_ne_bot : I ≠ ⊥) : I.comap (algebraMap R (integralClosure R S)) ≠ ⊥ :=
   IsIntegralClosure.comap_ne_bot S I_ne_bot
 #align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_bot
 
-/- warning: ideal.integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integralClosure R S)} :
     I.comap (algebraMap R (integralClosure R S)) = ⊥ → I = ⊥ :=
   IsIntegralClosure.eq_bot_of_comap_eq_bot S
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
 
-/- warning: ideal.exists_ideal_over_prime_of_is_integral' -> Ideal.exists_ideal_over_prime_of_is_integral' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_is_integral'ₓ'. -/
 /-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
@@ -537,9 +405,6 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
 
 end
 
-/- warning: ideal.exists_ideal_over_prime_of_is_integral -> Ideal.exists_ideal_over_prime_of_isIntegral is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegralₓ'. -/
 /-- More general going-up theorem than `exists_ideal_over_prime_of_is_integral'`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?
   Not sure how best to write an ascending chain in Lean -/
@@ -563,12 +428,6 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     simpa [← RingHom.ker_eq_comap_bot] using hIP
 #align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegral
 
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-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_maximal_of_is_integral Ideal.exists_ideal_over_maximal_of_isIntegralₓ'. -/
 /-- `comap (algebra_map R S)` is a surjection from the max spec of `S` to max spec of `R`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)

61db041a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -83,8 +83,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
   by
   refine' p.rec_on_horner _ _ _
-  · intro h
-    contradiction
+  · intro h; contradiction
   · intro p a coeff_eq_zero a_ne_zero ih p_ne_zero hp
     refine' ⟨0, _, coeff_zero_mem_comap_of_root_mem hr hp⟩
     simp [coeff_eq_zero, a_ne_zero]

61db041a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -138,10 +138,7 @@ theorem quotient_mk_maps_eq (P : Ideal R[X]) :
 -/
 
 /- warning: ideal.exists_nonzero_mem_of_ne_bot -> Ideal.exists_nonzero_mem_of_ne_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : 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)))}, (Ne.{succ 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)))) P (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))))))) -> (forall (x : R), (Membership.Mem.{u1, u1} (Polynomial.{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))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SetLike.hasMem.{u1, 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)))) (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))) (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)))))) (coeFn.{succ u1, succ u1} (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))))) (fun (_x : 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))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{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))) x) P) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And (Membership.Mem.{u1, u1} (Polynomial.{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))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SetLike.hasMem.{u1, 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)))) (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))) (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)))))) p P) (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{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))) 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(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))) P)) (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) (Ideal.comap.{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))))) 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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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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 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R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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 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(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))) P)) (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) (Ideal.comap.{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))) P)) (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) (Ideal.comap.{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))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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))) P))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.exists_nonzero_mem_of_ne_bot Ideal.exists_nonzero_mem_of_ne_botₓ'. -/
 /-- This technical lemma asserts the existence of a polynomial `p` in an ideal `P ⊂ R[x]`
 that is non-zero in the quotient `R / (P ∩ R) [x]`.  The assumptions are equivalent to
@@ -163,10 +160,7 @@ theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀
 variable {p : Ideal R} {P : Ideal S}
 
 /- warning: ideal.comap_eq_of_scalar_tower_quotient -> Ideal.comap_eq_of_scalar_tower_quotient is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {P : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P)))] [_inst_5 : IsScalarTower.{u1, u1, u2} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Submodule.Quotient.hasSmul.{u1, u1} R R (CommRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (SMulZeroClass.toHasSmul.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddZeroClass.toHasZero.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (MulZeroClass.toHasZero.{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) p) (MulZeroOneClass.toMulZeroClass.{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) p) (MonoidWithZero.toMulZeroOneClass.{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) p) (Semiring.toMonoidWithZero.{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) p) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p))))))) (AddZeroClass.toHasZero.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) P) p)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {p : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {P : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : Algebra.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))] [_inst_5 : IsScalarTower.{u2, u2, u1} R (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Submodule.Quotient.hasSmul.{u2, u2} R R (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) p) (Algebra.toSMul.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))) _inst_4) (Submodule.Quotient.hasSmul'.{u1, u1, u2} S S (CommRing.toRing.{u1} S _inst_2) (Ring.toAddCommGroup.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) R (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (IsScalarTower.right.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) P)], (Function.Injective.{succ u2, succ u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S 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S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R 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(Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))))) (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))))) (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))) (RingHom.instRingHomClassRingHom.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))))))) (algebraMap.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))) _inst_4))) -> (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) P) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotientₓ'. -/
 /-- If there is an injective map `R/p → S/P` such that following diagram commutes:
 ```
@@ -261,10 +255,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_ze
 #align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem
 
 /- warning: ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff -> Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} S) (Set.booleanAlgebra.{u2} S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) J) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) I))) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) p) (OfNat.ofNat.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (OfNat.mk.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (Zero.zero.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (Exists.{1} Nat (fun (i : Nat) => Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p i) (SDiff.sdiff.{u1} (Set.{u1} R) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} R) (Set.booleanAlgebra.{u1} R)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f J)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (Set.instSDiffSet.{u2} S) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R 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(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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (Exists.{1} Nat (fun (i : Nat) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (SDiff.sdiff.{u1} (Set.{u1} R) (Set.instSDiffSet.{u1} R) (SetLike.coe.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f J)) (SetLike.coe.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiffₓ'. -/
 theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
@@ -291,10 +282,7 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
 #align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff
 
 /- warning: ideal.comap_lt_comap_of_root_mem_sdiff -> Ideal.comap_lt_comap_of_root_mem_sdiff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} S) (Set.booleanAlgebra.{u2} S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) 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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) p) (OfNat.ofNat.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (OfNat.mk.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (Zero.zero.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f J))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (Set.instSDiffSet.{u2} S) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) J) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) I))) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S 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(Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) 0 (Zero.toOfNat0.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLT.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f J))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
@@ -314,10 +302,7 @@ theorem mem_of_one_mem (h : (1 : S) ∈ I) (x) : x ∈ I :=
 #align ideal.mem_of_one_mem Ideal.mem_of_one_mem
 
 /- warning: ideal.comap_lt_comap_of_integral_mem_sdiff -> Ideal.comap_lt_comap_of_integral_mem_sdiff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [hI : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) I J) -> (forall {x : S}, (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) x (SDiff.sdiff.{u2} (Set.{u2} S) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} S) (Set.booleanAlgebra.{u2} S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) J) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) I))) -> (IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3 x) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLt.{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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) J)))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} {J : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [hI : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (LE.le.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Preorder.toLE.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.completeLattice.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) I J) -> (forall {x : S}, (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x (SDiff.sdiff.{u1} (Set.{u1} S) (Set.instSDiffSet.{u1} S) (SetLike.coe.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) J) (SetLike.coe.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) I))) -> (IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3 x) -> (LT.lt.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLT.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) J)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ : I ≤ J) {x : S}
     (mem : x ∈ (J : Set S) \ I) (integral : IsIntegral R x) :
@@ -444,10 +429,7 @@ variable (S) {A : Type _} [CommRing A]
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]
 
 /- warning: ideal.is_integral_closure.comap_lt_comap -> Ideal.IsIntegralClosure.comap_lt_comap is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))} {J : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))} [_inst_9 : Ideal.IsPrime.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I], (LT.lt.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Preorder.toHasLt.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (PartialOrder.toPreorder.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.completeLattice.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) I J) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLt.{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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) J))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u2}} [_inst_4 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))] [_inst_6 : Algebra.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u2, u3} R A S (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) (Algebra.toSMul.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u2, u1, u3} A R S _inst_1 (CommRing.toCommSemiring.{u2} A _inst_4) _inst_2 _inst_3 _inst_6] {I : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))} {J : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))} [_inst_9 : Ideal.IsPrime.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I], (LT.lt.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (Preorder.toLT.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (Submodule.completeLattice.{u2, u2} A A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))))) (Semiring.toModule.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))))))) I J) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLT.{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.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) I) (Ideal.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) J))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comapₓ'. -/
 theorem IsIntegralClosure.comap_lt_comap {I J : Ideal A} [I.IsPrime] (I_lt_J : I < J) :
     I.comap (algebraMap R A) < J.comap (algebraMap R A) :=
@@ -469,10 +451,7 @@ theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
 variable [IsDomain A]
 
 /- warning: ideal.is_integral_closure.comap_ne_bot -> Ideal.IsIntegralClosure.comap_ne_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_10 : Nontrivial.{u1} R] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))}, (Ne.{succ u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) I (Bot.bot.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.hasBot.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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))))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u1}} [_inst_4 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_6 : Algebra.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u2, u1, u3} R A S (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) (Algebra.toSMul.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u1, u2, u3} A R S _inst_1 (CommRing.toCommSemiring.{u1} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_10 : Nontrivial.{u2} R] {I : Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))}, (Ne.{succ u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) I (Bot.bot.{u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) (Submodule.instBotSubmodule.{u1, u1} A A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))) (Semiring.toModule.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))))) -> (Ne.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R A (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_botₓ'. -/
 theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot : I ≠ ⊥) :
     I.comap (algebraMap R A) ≠ ⊥ :=
@@ -481,10 +460,7 @@ theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot :
 #align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_bot
 
 /- warning: ideal.is_integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_10 : Nontrivial.{u1} R] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))}, (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) -> (Eq.{succ u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) I (Bot.bot.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.hasBot.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u1}} [_inst_4 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_6 : Algebra.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u2, u1, u3} R A S (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) (Algebra.toSMul.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u1, u2, u3} A R S _inst_1 (CommRing.toCommSemiring.{u1} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_10 : Nontrivial.{u2} R] {I : Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))}, (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R A (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) -> (Eq.{succ u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) I (Bot.bot.{u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) (Submodule.instBotSubmodule.{u1, u1} A A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))) (Semiring.toModule.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.eq_bot_of_comap_eq_bot Ideal.IsIntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
     I.comap (algebraMap R A) = ⊥ → I = ⊥ :=
@@ -494,10 +470,7 @@ theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
 end IsIntegralClosure
 
 /- warning: ideal.integral_closure.comap_lt_comap -> Ideal.IntegralClosure.comap_lt_comap is a dubious translation:
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(SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) 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_inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) J))
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-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {I : Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))} {J : Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))} [_inst_4 : Ideal.IsPrime.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I], (LT.lt.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Preorder.toLT.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Submodule.completeLattice.{u2, u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))))) (Semiring.toModule.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))))))) I J) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLT.{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.comap.{u1, u2, max u1 u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (RingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S 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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comapₓ'. -/
 theorem IntegralClosure.comap_lt_comap {I J : Ideal (integralClosure R S)} [I.IsPrime]
     (I_lt_J : I < J) :
@@ -506,10 +479,7 @@ theorem IntegralClosure.comap_lt_comap {I J : Ideal (integralClosure R S)} [I.Is
 #align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comap
 
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(CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) [_inst_4 : Ideal.IsPrime.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I], 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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.is_maximal_of_is_maximal_comap Ideal.IntegralClosure.isMaximal_of_isMaximal_comapₓ'. -/
 theorem IntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal (integralClosure R S)) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R (integralClosure R S)))) : IsMaximal I :=
@@ -521,10 +491,7 @@ section
 variable [IsDomain S]
 
 /- warning: ideal.integral_closure.comap_ne_bot -> Ideal.IntegralClosure.comap_ne_bot is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_botₓ'. -/
 theorem IntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal (integralClosure R S)}
     (I_ne_bot : I ≠ ⊥) : I.comap (algebraMap R (integralClosure R S)) ≠ ⊥ :=
@@ -532,10 +499,7 @@ theorem IntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal (integralClosure
 #align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_bot
 
 /- warning: ideal.integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integralClosure R S)} :
     I.comap (algebraMap R (integralClosure R S)) = ⊥ → I = ⊥ :=
@@ -575,10 +539,7 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
 end
 
 /- warning: ideal.exists_ideal_over_prime_of_is_integral -> Ideal.exists_ideal_over_prime_of_isIntegral is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_4 : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P] (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [_inst_5 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) P) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (Q : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => Exists.{0} (GE.ge.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) Q I) (fun (H : GE.ge.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) Q I) => And (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) Q) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Q) P)))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (forall (P : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) [_inst_4 : Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) P] (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [_inst_5 : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I) P) -> (Exists.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (fun (Q : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) => And (GE.ge.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Preorder.toLE.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.completeLattice.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) Q I) (And (Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) Q) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) Q) P)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegralₓ'. -/
 /-- More general going-up theorem than `exists_ideal_over_prime_of_is_integral'`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?

61db041a

bump to nightly-2023-05-25-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

2175c3c2

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.ideal.over
-! leanprover-community/mathlib commit 198cb64d5c961e1a8d0d3e219feb7058d5353861
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Localization.Integral
 /-!
 # Ideals over/under ideals
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file concerns ideals lying over other ideals.
 Let `f : R →+* S` be a ring homomorphism (typically a ring extension), `I` an ideal of `R` and
 `J` an ideal of `S`. We say `J` lies over `I` (and `I` under `J`) if `I` is the `f`-preimage of `J`.

198cb64d

bump to nightly-2023-05-23-16

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

869439c6

Diff

@@ -44,6 +44,12 @@ section CommRing
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
+/- warning: ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem -> Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {r : S}, (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (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))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {r : S}, (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (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))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))
+Case conversion may be inaccurate. Consider using '#align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_memₓ'. -/
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f :=
   by
@@ -52,11 +58,23 @@ theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p :
   exact I.mul_mem_left _ hr
 #align ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem
 
+/- warning: ideal.coeff_zero_mem_comap_of_root_mem -> Ideal.coeff_zero_mem_comap_of_root_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {r : S}, (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (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))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {r : S}, (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) -> (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))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))
+Case conversion may be inaccurate. Consider using '#align ideal.coeff_zero_mem_comap_of_root_mem Ideal.coeff_zero_mem_comap_of_root_memₓ'. -/
 theorem coeff_zero_mem_comap_of_root_mem {r : S} (hr : r ∈ I) {p : R[X]} (hp : p.eval₂ f r = 0) :
     p.coeff 0 ∈ I.comap f :=
   coeff_zero_mem_comap_of_root_mem_of_eval_mem hr (hp.symm ▸ I.zero_mem)
 #align ideal.coeff_zero_mem_comap_of_root_mem Ideal.coeff_zero_mem_comap_of_root_mem
 
+/- warning: ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem -> Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {r : S}, (forall {x : S}, (Eq.{succ u2} S (HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocRing.toMul.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))) x r) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) -> (Eq.{succ u2} S x (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CommSemiring.toCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))) -> (Exists.{1} Nat (fun (i : Nat) => And (Ne.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_memₓ'. -/
 theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     (r_non_zero_divisor : ∀ {x}, x * r = 0 → x = 0) (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
@@ -73,6 +91,7 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     refine' ⟨i + 1, _, _⟩ <;> simp [hi, mem]
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
 
+#print Ideal.injective_quotient_le_comap_map /-
 /-- Let `P` be an ideal in `R[x]`.  The map
 `R[x]/P → (R / (P ∩ R))[x] / (P / (P ∩ R))`
 is injective.
@@ -90,7 +109,9 @@ theorem injective_quotient_le_comap_map (P : Ideal R[X]) :
     polynomial_mem_ideal_of_coeff_mem_ideal P p fun n => quotient.eq_zero_iff_mem.mp _
   simpa only [coeff_map, coe_map_ring_hom] using ext_iff.mp (ideal.mem_bot.mp (mem_comap.mp hp)) n
 #align ideal.injective_quotient_le_comap_map Ideal.injective_quotient_le_comap_map
+-/
 
+#print Ideal.quotient_mk_maps_eq /-
 /-- The identity in this lemma asserts that the "obvious" square
 ```
     R    → (R / (P ∩ R))
@@ -111,7 +132,14 @@ theorem quotient_mk_maps_eq (P : Ideal R[X]) :
   repeat' rw [RingHom.coe_comp, Function.comp_apply]
   rw [quotient_map_mk, coe_map_ring_hom, map_C]
 #align ideal.quotient_mk_maps_eq Ideal.quotient_mk_maps_eq
+-/
 
+/- warning: ideal.exists_nonzero_mem_of_ne_bot -> Ideal.exists_nonzero_mem_of_ne_bot is a dubious translation:
+lean 3 declaration is
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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))) x) P) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => And 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(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)))))) p P) (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) p) 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(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))) P)) (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) (Ideal.comap.{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))))) 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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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P))))) 0 (OfNat.mk.{u1} (Polynomial.{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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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} 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R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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 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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))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P))))) (Polynomial.zero.{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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (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) (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{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)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{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))) P)))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : 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)))}, (Ne.{succ 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)))) P (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))))))) -> (forall (x : R), (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) x) (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)))) (SetLike.instMembership.{u1, 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)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.setLike.{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)))))) (FunLike.coe.{succ u1, succ u1, succ u1} (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))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (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))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{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)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (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))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (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))))) 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)))) (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))) x) P) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => And (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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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))) P))))))))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_nonzero_mem_of_ne_bot Ideal.exists_nonzero_mem_of_ne_botₓ'. -/
 /-- This technical lemma asserts the existence of a polynomial `p` in an ideal `P ⊂ R[x]`
 that is non-zero in the quotient `R / (P ∩ R) [x]`.  The assumptions are equivalent to
 `P ≠ 0` and `P ∩ R = (0)`.
@@ -131,6 +159,12 @@ theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀
 
 variable {p : Ideal R} {P : Ideal S}
 
+/- warning: ideal.comap_eq_of_scalar_tower_quotient -> Ideal.comap_eq_of_scalar_tower_quotient is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {P : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Algebra.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P)))] [_inst_5 : IsScalarTower.{u1, u1, u2} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Submodule.Quotient.hasSmul.{u1, u1} R R (CommRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p) (SMulZeroClass.toHasSmul.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddZeroClass.toHasZero.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (MulZeroClass.toHasZero.{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) p) (MulZeroOneClass.toMulZeroClass.{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) p) (MonoidWithZero.toMulZeroOneClass.{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) p) (Semiring.toMonoidWithZero.{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) p) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p))))))) (AddZeroClass.toHasZero.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toMonoidWithZero.{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) p) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)))) (AddZeroClass.toHasZero.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))))))) (Module.toMulActionWithZero.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P)))))) (Algebra.toModule.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))) _inst_4))))) (Submodule.Quotient.hasSmul'.{u2, u2, u1} S S (CommRing.toRing.{u2} S _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) R (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S 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(AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3))))) (IsScalarTower.right.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) P)], (Function.Injective.{succ u1, succ u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R 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(Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))) (fun (_x : RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P)) (RingHom.hasCoeToFun.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (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) p) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))) (algebraMap.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))) _inst_4))) -> (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) P) p)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {p : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {P : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : Algebra.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))] [_inst_5 : IsScalarTower.{u2, u2, u1} R (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Submodule.Quotient.hasSmul.{u2, u2} R R (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) p) (Algebra.toSMul.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) 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(CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))))) (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))) (RingHom.instRingHomClassRingHom.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P)))))))) (algebraMap.{u2, u1} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) p) (Ideal.Quotient.commRing.{u2} R _inst_1 p)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) P) (Ideal.Quotient.commRing.{u1} S _inst_2 P))) _inst_4))) -> (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) P) p)
+Case conversion may be inaccurate. Consider using '#align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotientₓ'. -/
 /-- If there is an injective map `R/p → S/P` such that following diagram commutes:
 ```
 R   → S
@@ -152,41 +186,57 @@ theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S 
     rw [hx, RingHom.map_zero]
 #align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotient
 
+/- warning: ideal.quotient.algebra_quotient_of_le_comap -> Ideal.Quotient.algebraQuotientOfLeComap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {p : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {P : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))}, (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) p (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f P)) -> (Algebra.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {P : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))}, (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) p (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f P)) -> (Algebra.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) p) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) P) (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) p) (Ideal.Quotient.commRing.{u1} R _inst_1 p)) (CommSemiring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) P) (CommRing.toCommSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) P) (Ideal.Quotient.commRing.{u2} S _inst_2 P))))
+Case conversion may be inaccurate. Consider using '#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComapₓ'. -/
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`. -/
 def Quotient.algebraQuotientOfLeComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
   RingHom.toAlgebra <| quotientMap _ f h
 #align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComap
 
+#print Ideal.Quotient.algebraQuotientMapQuotient /-
 /-- `R / p` has a canonical map to `S / pS`. -/
 instance Quotient.algebraQuotientMapQuotient : Algebra (R ⧸ p) (S ⧸ map f p) :=
   quotient.algebra_quotient_of_le_comap le_comap_map
 #align ideal.quotient.algebra_quotient_map_quotient Ideal.Quotient.algebraQuotientMapQuotient
+-/
 
+#print Ideal.Quotient.algebraMap_quotient_map_quotient /-
 @[simp]
 theorem Quotient.algebraMap_quotient_map_quotient (x : R) :
     algebraMap (R ⧸ p) (S ⧸ map f p) (Quotient.mk p x) = Quotient.mk _ (f x) :=
   rfl
 #align ideal.quotient.algebra_map_quotient_map_quotient Ideal.Quotient.algebraMap_quotient_map_quotient
+-/
 
+#print Ideal.Quotient.mk_smul_mk_quotient_map_quotient /-
 @[simp]
 theorem Quotient.mk_smul_mk_quotient_map_quotient (x : R) (y : S) :
     Quotient.mk p x • Quotient.mk (map f p) y = Quotient.mk _ (f x * y) :=
   rfl
 #align ideal.quotient.mk_smul_mk_quotient_map_quotient Ideal.Quotient.mk_smul_mk_quotient_map_quotient
+-/
 
+#print Ideal.Quotient.tower_quotient_map_quotient /-
 instance Quotient.tower_quotient_map_quotient [Algebra R S] :
     IsScalarTower R (R ⧸ p) (S ⧸ map (algebraMap R S) p) :=
   IsScalarTower.of_algebraMap_eq fun x => by
     rw [quotient.algebra_map_eq, quotient.algebra_map_quotient_map_quotient,
       quotient.mk_algebra_map]
 #align ideal.quotient.tower_quotient_map_quotient Ideal.Quotient.tower_quotient_map_quotient
+-/
 
+#print Ideal.QuotientMapQuotient.isNoetherian /-
 instance QuotientMapQuotient.isNoetherian [Algebra R S] [IsNoetherian R S] (I : Ideal R) :
     IsNoetherian (R ⧸ I) (S ⧸ Ideal.map (algebraMap R S) I) :=
   isNoetherian_of_tower R <|
     isNoetherian_of_surjective S (Ideal.Quotient.mkₐ R _).toLinearMap <|
       LinearMap.range_eq_top.mpr Ideal.Quotient.mk_surjective
 #align ideal.quotient_map_quotient.is_noetherian Ideal.QuotientMapQuotient.isNoetherian
+-/
 
 end CommRing
 
@@ -194,6 +244,12 @@ section IsDomain
 
 variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
+/- warning: ideal.exists_coeff_ne_zero_mem_comap_of_root_mem -> Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {r : S}, (Ne.{succ u2} S r (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Exists.{1} Nat (fun (i : Nat) => And (Ne.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) (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))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p i) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {r : S}, (Ne.{succ u2} S r (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))) -> (Exists.{1} Nat (fun (i : Nat) => And (Ne.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_memₓ'. -/
 theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0)
     (hr : r ∈ I) {p : R[X]} :
     ∀ (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
@@ -201,6 +257,12 @@ theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_ze
     (fun _ h => Or.resolve_right (mul_eq_zero.mp h) r_ne_zero) hr
 #align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem
 
+/- warning: ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff -> Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) 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(CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) J) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S 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u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) p) (OfNat.ofNat.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (OfNat.mk.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (Zero.zero.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (Exists.{1} Nat (fun (i : Nat) => Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p i) (SDiff.sdiff.{u1} (Set.{u1} R) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} R) (Set.booleanAlgebra.{u1} R)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f J)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} R) (SetLike.Set.hasCoeT.{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))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (Set.instSDiffSet.{u2} S) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) J) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) I))) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) p) (OfNat.ofNat.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) 0 (Zero.toOfNat0.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (Exists.{1} Nat (fun (i : Nat) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p i) (SDiff.sdiff.{u1} (Set.{u1} R) (Set.instSDiffSet.{u1} R) (SetLike.coe.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f J)) (SetLike.coe.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiffₓ'. -/
 theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hpI : p.eval₂ f r ∈ I) : ∃ i, p.coeff i ∈ (J.comap f : Set R) \ I.comap f :=
@@ -225,6 +287,12 @@ theorem exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff [IsPrime I] (hIJ :
   simp [quotient.eq_zero_iff_mem]
 #align ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff
 
+/- warning: ideal.comap_lt_comap_of_root_mem_sdiff -> Ideal.comap_lt_comap_of_root_mem_sdiff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) 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(CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (OfNat.mk.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) 0 (Zero.zero.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) I) -> (LT.lt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLt.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f J))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} {J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))))) I J) -> (forall {r : S}, (Membership.mem.{u2, u2} S (Set.{u2} S) (Set.instMembershipSet.{u2} S) r (SDiff.sdiff.{u2} (Set.{u2} S) (Set.instSDiffSet.{u2} S) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) J) (SetLike.coe.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) I))) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.map.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))) (Ideal.Quotient.mk.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) p) (OfNat.ofNat.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) 0 (Zero.toOfNat0.{u1} (Polynomial.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I))))) (Polynomial.zero.{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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (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) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)) (Ideal.Quotient.commRing.{u1} R _inst_1 (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I)))))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) I) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLT.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f J))))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
     (hr : r ∈ (J : Set S) \ I) {p : R[X]} (p_ne_zero : p.map (Quotient.mk (I.comap f)) ≠ 0)
     (hp : p.eval₂ f r ∈ I) : I.comap f < J.comap f :=
@@ -232,10 +300,22 @@ theorem comap_lt_comap_of_root_mem_sdiff [I.IsPrime] (hIJ : I ≤ J) {r : S}
   SetLike.lt_iff_le_and_exists.mpr ⟨comap_mono hIJ, p.coeff i, hJ, hI⟩
 #align ideal.comap_lt_comap_of_root_mem_sdiff Ideal.comap_lt_comap_of_root_mem_sdiff
 
+/- warning: ideal.mem_of_one_mem -> Ideal.mem_of_one_mem is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {I : Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))}, (Membership.Mem.{u1, u1} S (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) I) -> (forall (x : S), Membership.Mem.{u1, u1} S (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x I)
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))}, (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) I) -> (forall (x : S), Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) x I)
+Case conversion may be inaccurate. Consider using '#align ideal.mem_of_one_mem Ideal.mem_of_one_memₓ'. -/
 theorem mem_of_one_mem (h : (1 : S) ∈ I) (x) : x ∈ I :=
   (I.eq_top_iff_one.mpr h).symm ▸ mem_top
 #align ideal.mem_of_one_mem Ideal.mem_of_one_mem
 
+/- warning: ideal.comap_lt_comap_of_integral_mem_sdiff -> Ideal.comap_lt_comap_of_integral_mem_sdiff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} {J : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [hI : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Preorder.toHasLe.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) I J) -> (forall {x : S}, (Membership.Mem.{u2, u2} S (Set.{u2} S) (Set.hasMem.{u2} S) x (SDiff.sdiff.{u2} (Set.{u2} S) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} S) (Set.booleanAlgebra.{u2} S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) J) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (HasLiftT.mk.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (CoeTCₓ.coe.{succ u2, succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Set.{u2} S) (SetLike.Set.hasCoeT.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))) I))) -> (IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3 x) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLt.{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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) J)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} {J : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [hI : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (LE.le.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Preorder.toLE.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.completeLattice.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) I J) -> (forall {x : S}, (Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x (SDiff.sdiff.{u1} (Set.{u1} S) (Set.instSDiffSet.{u1} S) (SetLike.coe.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) J) (SetLike.coe.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) I))) -> (IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3 x) -> (LT.lt.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLT.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) J)))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiffₓ'. -/
 theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ : I ≤ J) {x : S}
     (mem : x ∈ (J : Set S) \ I) (integral : IsIntegral R x) :
     I.comap (algebraMap R S) < J.comap (algebraMap R S) :=
@@ -250,12 +330,24 @@ theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ
   convert I.zero_mem
 #align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiff
 
+/- warning: ideal.comap_ne_bot_of_root_mem -> Ideal.comap_ne_bot_of_root_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))} {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {r : S}, (Ne.{succ u2} S r (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I) (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)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))} {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_3 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {r : S}, (Ne.{succ u2} S r (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))) -> (Membership.mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) r I) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) -> (Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) f r p) (OfNat.ofNat.{u2} S 0 (Zero.toOfNat0.{u2} S (CommMonoidWithZero.toZero.{u2} S (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} S (IsDomain.toCancelCommMonoidWithZero.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3)))))) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) f I) (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)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.comap_ne_bot_of_root_mem Ideal.comap_ne_bot_of_root_memₓ'. -/
 theorem comap_ne_bot_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0) (hr : r ∈ I) {p : R[X]}
     (p_ne_zero : p ≠ 0) (hp : p.eval₂ f r = 0) : I.comap f ≠ ⊥ := fun h =>
   let ⟨i, hi, mem⟩ := exists_coeff_ne_zero_mem_comap_of_root_mem r_ne_zero hr p_ne_zero hp
   absurd (mem_bot.mp (eq_bot_iff.mp h mem)) hi
 #align ideal.comap_ne_bot_of_root_mem Ideal.comap_ne_bot_of_root_mem
 
+/- warning: ideal.is_maximal_of_is_integral_of_is_maximal_comap -> Ideal.isMaximal_of_isIntegral_of_isMaximal_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [_inst_4 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I)) -> (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (forall (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [_inst_4 : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (Ideal.IsMaximal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I)) -> (Ideal.IsMaximal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I))
+Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_of_is_integral_of_is_maximal_comap Ideal.isMaximal_of_isIntegral_of_isMaximal_comapₓ'. -/
 theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.IsIntegral R S)
     (I : Ideal S) [I.IsPrime] (hI : IsMaximal (I.comap (algebraMap R S))) : IsMaximal I :=
   ⟨⟨mt comap_eq_top_iff.mpr hI.1.1, fun J I_lt_J =>
@@ -264,6 +356,12 @@ theorem isMaximal_of_isIntegral_of_isMaximal_comap [Algebra R S] (hRS : Algebra.
         hI.1.2 _ (comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (hRS x))⟩⟩
 #align ideal.is_maximal_of_is_integral_of_is_maximal_comap Ideal.isMaximal_of_isIntegral_of_isMaximal_comap
 
+/- warning: ideal.is_maximal_of_is_integral_of_is_maximal_comap' -> Ideal.isMaximal_of_isIntegral_of_isMaximal_comap' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))), (RingHom.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) f) -> (forall (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hI' : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))) f I)) -> (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))), (RingHom.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) f) -> (forall (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [hI' : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (Ideal.IsMaximal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f I)) -> (Ideal.IsMaximal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I))
+Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_of_is_integral_of_is_maximal_comap' Ideal.isMaximal_of_isIntegral_of_isMaximal_comap'ₓ'. -/
 theorem isMaximal_of_isIntegral_of_isMaximal_comap' (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S)
     [hI' : I.IsPrime] (hI : IsMaximal (I.comap f)) : IsMaximal I :=
   @isMaximal_of_isIntegral_of_isMaximal_comap R _ S _ f.toAlgebra hf I hI' hI
@@ -271,17 +369,35 @@ theorem isMaximal_of_isIntegral_of_isMaximal_comap' (f : R →+* S) (hf : f.IsIn
 
 variable [Algebra R S]
 
+/- warning: ideal.comap_ne_bot_of_algebraic_mem -> Ideal.comap_ne_bot_of_algebraic_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {x : S}, (Ne.{succ u2} S x (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) x I) -> (IsAlgebraic.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3 x) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ideal.comap_ne_bot_of_algebraic_mem Ideal.comap_ne_bot_of_algebraic_memₓ'. -/
 theorem comap_ne_bot_of_algebraic_mem [IsDomain S] {x : S} (x_ne_zero : x ≠ 0) (x_mem : x ∈ I)
     (hx : IsAlgebraic R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   let ⟨p, p_ne_zero, hp⟩ := hx
   comap_ne_bot_of_root_mem x_ne_zero x_mem p_ne_zero hp
 #align ideal.comap_ne_bot_of_algebraic_mem Ideal.comap_ne_bot_of_algebraic_mem
 
+/- warning: ideal.comap_ne_bot_of_integral_mem -> Ideal.comap_ne_bot_of_integral_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Nontrivial.{u1} R] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {x : S}, (Ne.{succ u2} S x (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))))) -> (Membership.Mem.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) x I) -> (IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3 x) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ideal.comap_ne_bot_of_integral_mem Ideal.comap_ne_bot_of_integral_memₓ'. -/
 theorem comap_ne_bot_of_integral_mem [Nontrivial R] [IsDomain S] {x : S} (x_ne_zero : x ≠ 0)
     (x_mem : x ∈ I) (hx : IsIntegral R x) : I.comap (algebraMap R S) ≠ ⊥ :=
   comap_ne_bot_of_algebraic_mem x_ne_zero x_mem (hx.IsAlgebraic R)
 #align ideal.comap_ne_bot_of_integral_mem Ideal.comap_ne_bot_of_integral_mem
 
+/- warning: ideal.eq_bot_of_comap_eq_bot -> Ideal.eq_bot_of_comap_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] {I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))} [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : Nontrivial.{u1} R] [_inst_5 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) -> (Eq.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) I (Bot.bot.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.hasBot.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))} [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : Nontrivial.{u2} R] [_inst_5 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) -> (Eq.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) I (Bot.bot.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.instBotSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align ideal.eq_bot_of_comap_eq_bot Ideal.eq_bot_of_comap_eq_botₓ'. -/
 theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsIntegral R S)
     (hI : I.comap (algebraMap R S) = ⊥) : I = ⊥ :=
   by
@@ -291,6 +407,12 @@ theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsInte
   · exact absurd hI (comap_ne_bot_of_integral_mem hx0 hx (hRS x))
 #align ideal.eq_bot_of_comap_eq_bot Ideal.eq_bot_of_comap_eq_bot
 
+/- warning: ideal.is_maximal_comap_of_is_integral_of_is_maximal -> Ideal.isMaximal_comap_of_isIntegral_of_isMaximal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hI : Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (forall (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [hI : Ideal.IsMaximal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], Ideal.IsMaximal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I))
+Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximalₓ'. -/
 theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S) (I : Ideal S)
     [hI : I.IsMaximal] : IsMaximal (I.comap (algebraMap R S)) :=
   by
@@ -301,6 +423,12 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
       algebra_map_quotient_injective (by rwa [← quotient.maximal_ideal_iff_is_field_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
+/- warning: ideal.is_maximal_comap_of_is_integral_of_is_maximal' -> Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))), (RingHom.IsIntegral.{u1, u2} R S _inst_4 (CommRing.toRing.{u2} S _inst_5) f) -> (forall (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))), (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) I) -> (Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (RingHom.ringHomClass.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f I)))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))), (RingHom.IsIntegral.{u2, u1} R S _inst_4 (CommRing.toRing.{u1} S _inst_5) f) -> (forall (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))), (Ideal.IsMaximal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) I) -> (Ideal.IsMaximal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) f I)))
+Case conversion may be inaccurate. Consider using '#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'ₓ'. -/
 theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
@@ -312,12 +440,24 @@ variable (S) {A : Type _} [CommRing A]
 
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]
 
+/- warning: ideal.is_integral_closure.comap_lt_comap -> Ideal.IsIntegralClosure.comap_lt_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))} {J : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))} [_inst_9 : Ideal.IsPrime.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I], (LT.lt.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Preorder.toHasLt.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (PartialOrder.toPreorder.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (CompleteSemilatticeInf.toPartialOrder.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.completeLattice.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) I J) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toHasLt.{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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) J))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u2}} [_inst_4 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))] [_inst_6 : Algebra.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u2, u3} R A S (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) (Algebra.toSMul.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u2, u1, u3} A R S _inst_1 (CommRing.toCommSemiring.{u2} A _inst_4) _inst_2 _inst_3 _inst_6] {I : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))} {J : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))} [_inst_9 : Ideal.IsPrime.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I], (LT.lt.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (Preorder.toLT.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) (Submodule.completeLattice.{u2, u2} A A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))))) (Semiring.toModule.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))))))) I J) -> (LT.lt.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLT.{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.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) I) (Ideal.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) J))
+Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comapₓ'. -/
 theorem IsIntegralClosure.comap_lt_comap {I J : Ideal A} [I.IsPrime] (I_lt_J : I < J) :
     I.comap (algebraMap R A) < J.comap (algebraMap R A) :=
   let ⟨I_le_J, x, hxJ, hxI⟩ := SetLike.lt_iff_le_and_exists.mp I_lt_J
   comap_lt_comap_of_integral_mem_sdiff I_le_J ⟨hxJ, hxI⟩ (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_lt_comap Ideal.IsIntegralClosure.comap_lt_comap
 
+/- warning: ideal.is_integral_closure.is_maximal_of_is_maximal_comap -> Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] (I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) [_inst_9 : Ideal.IsPrime.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I)) -> (Ideal.IsMaximal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u2}} [_inst_4 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))] [_inst_6 : Algebra.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u2, u3} R A S (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) (Algebra.toSMul.{u2, u3} A S (CommRing.toCommSemiring.{u2} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u1, u3} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u2, u1, u3} A R S _inst_1 (CommRing.toCommSemiring.{u2} A _inst_4) _inst_2 _inst_3 _inst_6] (I : Ideal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4))) [_inst_9 : Ideal.IsPrime.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) _inst_5) I)) -> (Ideal.IsMaximal.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_4)) I)
+Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.is_maximal_of_is_maximal_comap Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comapₓ'. -/
 theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R A))) : IsMaximal I :=
   isMaximal_of_isIntegral_of_isMaximal_comap (fun x => IsIntegralClosure.isIntegral R S x) I hI
@@ -325,12 +465,24 @@ theorem IsIntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal A) [I.IsPrime]
 
 variable [IsDomain A]
 
+/- warning: ideal.is_integral_closure.comap_ne_bot -> Ideal.IsIntegralClosure.comap_ne_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_10 : Nontrivial.{u1} R] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))}, (Ne.{succ u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) I (Bot.bot.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.hasBot.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u1}} [_inst_4 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_6 : Algebra.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u2, u1, u3} R A S (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) (Algebra.toSMul.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u1, u2, u3} A R S _inst_1 (CommRing.toCommSemiring.{u1} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_10 : Nontrivial.{u2} R] {I : Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))}, (Ne.{succ u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) I (Bot.bot.{u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) (Submodule.instBotSubmodule.{u1, u1} A A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))) (Semiring.toModule.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))))) -> (Ne.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R A (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_botₓ'. -/
 theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot : I ≠ ⊥) :
     I.comap (algebraMap R A) ≠ ⊥ :=
   let ⟨x, x_mem, x_ne_zero⟩ := I.ne_bot_iff.mp I_ne_bot
   comap_ne_bot_of_integral_mem x_ne_zero x_mem (IsIntegralClosure.isIntegral R S x)
 #align ideal.is_integral_closure.comap_ne_bot Ideal.IsIntegralClosure.comap_ne_bot
 
+/- warning: ideal.is_integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Type.{u2}) [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_6 : Algebra.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : IsScalarTower.{u1, u3, u2} R A S (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} A S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} A S (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} A S (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u3, u2} A S (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u3, u2} A S (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)))))] [_inst_8 : IsIntegralClosure.{u3, u1, u2} A R S _inst_1 (CommRing.toCommSemiring.{u3} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] [_inst_10 : Nontrivial.{u1} R] {I : Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))}, (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u3, max u1 u3} R A (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (RingHom.ringHomClass.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))) (algebraMap.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) I) (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.hasBot.{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)))))) -> (Eq.{succ u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) I (Bot.bot.{u3} (Ideal.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))) (Submodule.hasBot.{u3, u3} A A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Semiring.toModule.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Type.{u3}) [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] {A : Type.{u1}} [_inst_4 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_6 : Algebra.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : IsScalarTower.{u2, u1, u3} R A S (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) (Algebra.toSMul.{u1, u3} A S (CommRing.toCommSemiring.{u1} A _inst_4) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_6) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)] [_inst_8 : IsIntegralClosure.{u1, u2, u3} A R S _inst_1 (CommRing.toCommSemiring.{u1} A _inst_4) _inst_2 _inst_3 _inst_6] [_inst_9 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))] [_inst_10 : Nontrivial.{u2} R] {I : Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))}, (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R A (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) _inst_5) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) -> (Eq.{succ u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) I (Bot.bot.{u1} (Ideal.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))) (Submodule.instBotSubmodule.{u1, u1} A A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))) (Semiring.toModule.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_4))))))
+Case conversion may be inaccurate. Consider using '#align ideal.is_integral_closure.eq_bot_of_comap_eq_bot Ideal.IsIntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
     I.comap (algebraMap R A) = ⊥ → I = ⊥ :=
   imp_of_not_imp_not _ _ (IsIntegralClosure.comap_ne_bot S)
@@ -338,12 +490,24 @@ theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
 
 end IsIntegralClosure
 
+/- warning: ideal.integral_closure.comap_lt_comap -> Ideal.IntegralClosure.comap_lt_comap is a dubious translation:
+lean 3 declaration is
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Ideal.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))} [_inst_4 : Ideal.IsPrime.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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.comap.{u1, u2, max u1 u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.ringHomClass.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) I) (Ideal.comap.{u1, u2, max u1 u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.ringHomClass.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) J))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] {I : Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))} {J : Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))} [_inst_4 : Ideal.IsPrime.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I], (LT.lt.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Preorder.toLT.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S 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(CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Ideal.comap.{u1, u2, max u1 u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (RingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) I) (Ideal.comap.{u1, u2, max u1 u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (RingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) J))
+Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comapₓ'. -/
 theorem IntegralClosure.comap_lt_comap {I J : Ideal (integralClosure R S)} [I.IsPrime]
     (I_lt_J : I < J) :
     I.comap (algebraMap R (integralClosure R S)) < J.comap (algebraMap R (integralClosure R S)) :=
   IsIntegralClosure.comap_lt_comap S I_lt_J
 #align ideal.integral_closure.comap_lt_comap Ideal.IntegralClosure.comap_lt_comap
 
+/- warning: ideal.integral_closure.is_maximal_of_is_maximal_comap -> Ideal.IntegralClosure.isMaximal_of_isMaximal_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] (I : Ideal.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) [_inst_4 : 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_inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) I)) -> (Ideal.IsMaximal.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] (I : Ideal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) [_inst_4 : Ideal.IsPrime.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I], (Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.comap.{u1, u2, max u1 u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (RingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (RingHom.instRingHomClassRingHom.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (CommRing.toCommSemiring.{u1} R _inst_1) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) I)) -> (Ideal.IsMaximal.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) x (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) I)
+Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.is_maximal_of_is_maximal_comap Ideal.IntegralClosure.isMaximal_of_isMaximal_comapₓ'. -/
 theorem IntegralClosure.isMaximal_of_isMaximal_comap (I : Ideal (integralClosure R S)) [I.IsPrime]
     (hI : IsMaximal (I.comap (algebraMap R (integralClosure R S)))) : IsMaximal I :=
   IsIntegralClosure.isMaximal_of_isMaximal_comap S I hI
@@ -353,16 +517,34 @@ section
 
 variable [IsDomain S]
 
+/- warning: ideal.integral_closure.comap_ne_bot -> Ideal.IntegralClosure.comap_ne_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_5 : Nontrivial.{u1} R] {I : Ideal.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) S (Subalgebra.setLike.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.toSemiring.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : Nontrivial.{u2} R] {I : Ideal.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S 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+Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_botₓ'. -/
 theorem IntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal (integralClosure R S)}
     (I_ne_bot : I ≠ ⊥) : I.comap (algebraMap R (integralClosure R S)) ≠ ⊥ :=
   IsIntegralClosure.comap_ne_bot S I_ne_bot
 #align ideal.integral_closure.comap_ne_bot Ideal.IntegralClosure.comap_ne_bot
 
+/- warning: ideal.integral_closure.eq_bot_of_comap_eq_bot -> Ideal.IntegralClosure.eq_bot_of_comap_eq_bot is a dubious translation:
+lean 3 declaration is
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(CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3 (integralClosure.{u1, u2} R S _inst_1 _inst_2 _inst_3))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_5 : Nontrivial.{u2} R] {I : Ideal.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))}, (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (RingHom.{u2, u1} R (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} R (Subtype.{succ 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u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3)))) (algebraMap.{u2, u1} R (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (CommRing.toCommSemiring.{u2} R _inst_1) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3)) (Subalgebra.algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) I) (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) -> (Eq.{succ u1} (Ideal.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) I (Bot.bot.{u1} (Ideal.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Submodule.instBotSubmodule.{u1, u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))))) (Semiring.toModule.{u1} (Subtype.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) x (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))) (Subalgebra.toSemiring.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3 (integralClosure.{u2, u1} R S _inst_1 _inst_2 _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_botₓ'. -/
 theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integralClosure R S)} :
     I.comap (algebraMap R (integralClosure R S)) = ⊥ → I = ⊥ :=
   IsIntegralClosure.eq_bot_of_comap_eq_bot S
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
 
+/- warning: ideal.exists_ideal_over_prime_of_is_integral' -> Ideal.exists_ideal_over_prime_of_is_integral' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_5 : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P], (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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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)))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) P) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (Q : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => And (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) Q) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Q) P))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_4 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (forall (P : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) [_inst_5 : Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) P], (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3)) P) -> (Exists.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (fun (Q : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) => And (Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) Q) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) Q) P))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_is_integral'ₓ'. -/
 /-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
@@ -389,6 +571,12 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
 
 end
 
+/- warning: ideal.exists_ideal_over_prime_of_is_integral -> Ideal.exists_ideal_over_prime_of_isIntegral is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [_inst_4 : Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P] (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [_inst_5 : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) I], (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} 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(Submodule.completeLattice.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))))) Q I) => And (Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) Q) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Q) P)))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))], (Algebra.IsIntegral.{u2, u1} R S _inst_1 (CommRing.toRing.{u1} S _inst_2) _inst_3) -> (forall (P : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) [_inst_4 : Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) P] (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [_inst_5 : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) I], (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) I) P) -> (Exists.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (fun (Q : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) => And (GE.ge.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Preorder.toLE.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.completeLattice.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) Q I) (And (Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) Q) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.comap.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) _inst_3) Q) P)))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegralₓ'. -/
 /-- More general going-up theorem than `exists_ideal_over_prime_of_is_integral'`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?
   Not sure how best to write an ascending chain in Lean -/
@@ -412,6 +600,12 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     simpa [← RingHom.ker_eq_comap_bot] using hIP
 #align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegral
 
+/- warning: ideal.exists_ideal_over_maximal_of_is_integral -> Ideal.exists_ideal_over_maximal_of_isIntegral is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_4 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) [P_max : Ideal.IsMaximal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P], (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))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{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)))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3)) P) -> (Exists.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (fun (Q : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) => And (Ideal.IsMaximal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) Q) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) Q) P))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_4 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))], (Algebra.IsIntegral.{u1, u2} R S _inst_1 (CommRing.toRing.{u2} S _inst_2) _inst_3) -> (forall (P : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) [P_max : Ideal.IsMaximal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) P], (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)))))))) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3)) P) -> (Exists.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (fun (Q : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) => And (Ideal.IsMaximal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) Q) (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) Q) P))))
+Case conversion may be inaccurate. Consider using '#align ideal.exists_ideal_over_maximal_of_is_integral Ideal.exists_ideal_over_maximal_of_isIntegralₓ'. -/
 /-- `comap (algebra_map R S)` is a surjection from the max spec of `S` to max spec of `R`.
 `hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)

198cb64d

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -79,8 +79,8 @@ is injective.
 -/
 theorem injective_quotient_le_comap_map (P : Ideal R[X]) :
     Function.Injective
-      ((map (mapRingHom (Quotient.mk (P.comap (c : R →+* R[X])))) P).quotientMap
-        (mapRingHom (Quotient.mk (P.comap (c : R →+* R[X])))) le_comap_map) :=
+      ((map (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) P).quotientMap
+        (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) le_comap_map) :=
   by
   refine' quotient_map_injective' (le_of_eq _)
   rw [comap_map_of_surjective (map_ring_hom (Quotient.mk' (P.comap (C : R →+* R[X]))))
@@ -101,11 +101,11 @@ commutes.  It is used, for instance, in the proof of `quotient_mk_comp_C_is_inte
 in the file `ring_theory/jacobson`.
 -/
 theorem quotient_mk_maps_eq (P : Ideal R[X]) :
-    ((Quotient.mk (map (mapRingHom (Quotient.mk (P.comap (c : R →+* R[X])))) P)).comp c).comp
-        (Quotient.mk (P.comap (c : R →+* R[X]))) =
-      ((map (mapRingHom (Quotient.mk (P.comap (c : R →+* R[X])))) P).quotientMap
-            (mapRingHom (Quotient.mk (P.comap (c : R →+* R[X])))) le_comap_map).comp
-        ((Quotient.mk P).comp c) :=
+    ((Quotient.mk (map (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) P)).comp C).comp
+        (Quotient.mk (P.comap (C : R →+* R[X]))) =
+      ((map (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) P).quotientMap
+            (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) le_comap_map).comp
+        ((Quotient.mk P).comp C) :=
   by
   refine' RingHom.ext fun x => _
   repeat' rw [RingHom.coe_comp, Function.comp_apply]
@@ -116,8 +116,8 @@ theorem quotient_mk_maps_eq (P : Ideal R[X]) :
 that is non-zero in the quotient `R / (P ∩ R) [x]`.  The assumptions are equivalent to
 `P ≠ 0` and `P ∩ R = (0)`.
 -/
-theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀ x : R, c x ∈ P → x = 0) :
-    ∃ p : R[X], p ∈ P ∧ Polynomial.map (Quotient.mk (P.comap (c : R →+* R[X]))) p ≠ 0 :=
+theorem exists_nonzero_mem_of_ne_bot {P : Ideal R[X]} (Pb : P ≠ ⊥) (hP : ∀ x : R, C x ∈ P → x = 0) :
+    ∃ p : R[X], p ∈ P ∧ Polynomial.map (Quotient.mk (P.comap (C : R →+* R[X]))) p ≠ 0 :=
   by
   obtain ⟨m, hm⟩ := Submodule.nonzero_mem_of_bot_lt (bot_lt_iff_ne_bot.mpr Pb)
   refine' ⟨m, Submodule.coe_mem m, fun pp0 => hm (submodule.coe_eq_zero.mp _)⟩

198cb64d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

198cb64d

chore: remove remaining cdots that were not · (#12146)

A simple replacement . --> ·.

See #12143 for the source of these replacements.

8a7f8422

Diff

@@ -396,7 +396,7 @@ theorem exists_ideal_over_prime_of_isIntegral_of_isPrime
   refine' _root_.trans _ (_root_.trans (congr_arg (comap (Ideal.Quotient.mk
     (comap (algebraMap R S) I))) hQ') _)
   · rw [comap_comap]
-    exact congr_arg (comap . Q') (RingHom.ext fun r => rfl)
+    exact congr_arg (comap · Q') (RingHom.ext fun r => rfl)
   · refine' _root_.trans (comap_map_of_surjective _ Quotient.mk_surjective _) (sup_eq_left.2 _)
     simpa [← RingHom.ker_eq_comap_bot] using hIP

198cb64d

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

08686b25

Diff

@@ -410,7 +410,7 @@ lemma exists_ideal_comap_le_prime (P : Ideal R) [P.IsPrime]
     rintro _ ⟨⟨x, hx : x ∉ P, rfl⟩, hx'⟩
     exact (hx (hI hx')).elim
   have : Iₚ ≠ ⊤ := by
-    rw [Ne.def, Ideal.eq_top_iff_one, IsLocalization.mem_map_algebraMap_iff
+    rw [Ne, Ideal.eq_top_iff_one, IsLocalization.mem_map_algebraMap_iff
       (Algebra.algebraMapSubmonoid S P.primeCompl) Sₚ, not_exists]
     simp only [one_mul, IsLocalization.eq_iff_exists (Algebra.algebraMapSubmonoid S P.primeCompl),
       not_exists]

198cb64d

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -296,7 +296,6 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type*} [CommRing R] [
 section IsIntegralClosure
 
 variable (S) {A : Type*} [CommRing A]
-
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]
 
 theorem IsIntegralClosure.comap_lt_comap {I J : Ideal A} [I.IsPrime] (I_lt_J : I < J) :

198cb64d

style: reduce spacing variation in "porting note" comments (#10886)

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.

86b84c52

Diff

@@ -320,7 +320,7 @@ theorem IsIntegralClosure.comap_ne_bot [Nontrivial R] {I : Ideal A} (I_ne_bot :
 
 theorem IsIntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal A} :
     I.comap (algebraMap R A) = ⊥ → I = ⊥ := by
-  -- Porting note : `imp_of_not_imp_not` seems not existing
+  -- Porting note: `imp_of_not_imp_not` seems not existing
   contrapose; exact (IsIntegralClosure.comap_ne_bot S)
 #align ideal.is_integral_closure.eq_bot_of_comap_eq_bot Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot

198cb64d

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

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

This follows on from #6964.

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

a13e8040

Diff

@@ -406,12 +406,12 @@ lemma exists_ideal_comap_le_prime (P : Ideal R) [P.IsPrime]
     ∃ Q ≥ I, Q.IsPrime ∧ Q.comap (algebraMap R S) ≤ P := by
   let Sₚ := Localization (Algebra.algebraMapSubmonoid S P.primeCompl)
   let Iₚ := I.map (algebraMap S Sₚ)
-  have hI' : Disjoint (Algebra.algebraMapSubmonoid S P.primeCompl : Set S) I
-  · rw [Set.disjoint_iff]
+  have hI' : Disjoint (Algebra.algebraMapSubmonoid S P.primeCompl : Set S) I := by
+    rw [Set.disjoint_iff]
     rintro _ ⟨⟨x, hx : x ∉ P, rfl⟩, hx'⟩
     exact (hx (hI hx')).elim
-  have : Iₚ ≠ ⊤
-  · rw [Ne.def, Ideal.eq_top_iff_one, IsLocalization.mem_map_algebraMap_iff
+  have : Iₚ ≠ ⊤ := by
+    rw [Ne.def, Ideal.eq_top_iff_one, IsLocalization.mem_map_algebraMap_iff
       (Algebra.algebraMapSubmonoid S P.primeCompl) Sₚ, not_exists]
     simp only [one_mul, IsLocalization.eq_iff_exists (Algebra.algebraMapSubmonoid S P.primeCompl),
       not_exists]

198cb64d

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9215)

Follow-up #9184

ef974f86

Diff

@@ -55,7 +55,7 @@ theorem coeff_zero_mem_comap_of_root_mem {r : S} (hr : r ∈ I) {p : R[X]} (hp :
 
 theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     (r_non_zero_divisor : ∀ {x}, x * r = 0 → x = 0) (hr : r ∈ I) {p : R[X]} :
-    ∀ (_ : p ≠ 0) (_ : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f := by
+    p ≠ 0 → p.eval₂ f r = 0 → ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f := by
   refine' p.recOnHorner _ _ _
   · intro h
     contradiction
@@ -194,7 +194,7 @@ variable {S : Type*} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
 theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0)
     (hr : r ∈ I) {p : R[X]} :
-    ∀ (_ : p ≠ 0) (_ : p.eval₂ f r = 0), ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
+    p ≠ 0 → p.eval₂ f r = 0 → ∃ i, p.coeff i ≠ 0 ∧ p.coeff i ∈ I.comap f :=
   exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
     (fun {_} h => Or.resolve_right (mul_eq_zero.mp h) r_ne_zero) hr
 #align ideal.exists_coeff_ne_zero_mem_comap_of_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem

198cb64d

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -370,7 +370,7 @@ theorem exists_ideal_over_prime_of_isIntegral_of_isDomain (H : Algebra.IsIntegra
   refine' ⟨comap (algebraMap S Sₚ) Qₚ, ⟨comap_isPrime _ Qₚ, _⟩⟩
   convert Localization.AtPrime.comap_maximalIdeal (I := P)
   rw [comap_comap, ← LocalRing.eq_maximalIdeal Qₚ_max,
-    ←@IsLocalization.map_comp (P := S) (Q := Sₚ) (g := algebraMap R S)
+    ← @IsLocalization.map_comp (P := S) (Q := Sₚ) (g := algebraMap R S)
     (M := P.primeCompl) (T := Algebra.algebraMapSubmonoid S P.primeCompl) (S := Rₚ) _
     _ _ _ _ _ (fun p hp => Algebra.mem_algebraMapSubmonoid_of_mem ⟨p, hp⟩) _ _]
   rfl

198cb64d

feat: Relax arguments of going-up theorems. (#8645)

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

88b4f4c7

Diff

@@ -353,7 +353,7 @@ theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integr
 
 /-- `comap (algebraMap R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebraMap R S).ker ≤ P` is a slight generalization of the extension being injective -/
-theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P : Ideal R)
+theorem exists_ideal_over_prime_of_isIntegral_of_isDomain (H : Algebra.IsIntegral R S) (P : Ideal R)
     [IsPrime P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   have hP0 : (0 : S) ∉ Algebra.algebraMapSubmonoid S P.primeCompl := by
@@ -374,18 +374,19 @@ theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P :
     (M := P.primeCompl) (T := Algebra.algebraMapSubmonoid S P.primeCompl) (S := Rₚ) _
     _ _ _ _ _ (fun p hp => Algebra.mem_algebraMapSubmonoid_of_mem ⟨p, hp⟩) _ _]
   rfl
-#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral'
+#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomain
 
 end
 
-/-- More general going-up theorem than `exists_ideal_over_prime_of_isIntegral'`.
+/-- More general going-up theorem than `exists_ideal_over_prime_of_isIntegral_of_isDomain`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?
   Not sure how best to write an ascending chain in Lean -/
-theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P : Ideal R) [IsPrime P]
+theorem exists_ideal_over_prime_of_isIntegral_of_isPrime
+    (H : Algebra.IsIntegral R S) (P : Ideal R) [IsPrime P]
     (I : Ideal S) [IsPrime I] (hIP : I.comap (algebraMap R S) ≤ P) :
     ∃ Q ≥ I, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   obtain ⟨Q' : Ideal (S ⧸ I), ⟨Q'_prime, hQ'⟩⟩ :=
-    @exists_ideal_over_prime_of_isIntegral' (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
+    @exists_ideal_over_prime_of_isIntegral_of_isDomain (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
       Ideal.quotientAlgebra _ H.quotient
       (map (Ideal.Quotient.mk (I.comap (algebraMap R S))) P)
       (map_isPrime_of_surjective Quotient.mk_surjective (by simp [hIP]))
@@ -399,17 +400,64 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     exact congr_arg (comap . Q') (RingHom.ext fun r => rfl)
   · refine' _root_.trans (comap_map_of_surjective _ Quotient.mk_surjective _) (sup_eq_left.2 _)
     simpa [← RingHom.ker_eq_comap_bot] using hIP
+
+lemma exists_ideal_comap_le_prime (P : Ideal R) [P.IsPrime]
+    (I : Ideal S) (hI : I.comap (algebraMap R S) ≤ P) :
+    ∃ Q ≥ I, Q.IsPrime ∧ Q.comap (algebraMap R S) ≤ P := by
+  let Sₚ := Localization (Algebra.algebraMapSubmonoid S P.primeCompl)
+  let Iₚ := I.map (algebraMap S Sₚ)
+  have hI' : Disjoint (Algebra.algebraMapSubmonoid S P.primeCompl : Set S) I
+  · rw [Set.disjoint_iff]
+    rintro _ ⟨⟨x, hx : x ∉ P, rfl⟩, hx'⟩
+    exact (hx (hI hx')).elim
+  have : Iₚ ≠ ⊤
+  · rw [Ne.def, Ideal.eq_top_iff_one, IsLocalization.mem_map_algebraMap_iff
+      (Algebra.algebraMapSubmonoid S P.primeCompl) Sₚ, not_exists]
+    simp only [one_mul, IsLocalization.eq_iff_exists (Algebra.algebraMapSubmonoid S P.primeCompl),
+      not_exists]
+    exact fun x c ↦ hI'.ne_of_mem (mul_mem c.2 x.2.2) (I.mul_mem_left c x.1.2)
+  obtain ⟨M, hM, hM'⟩ := Ideal.exists_le_maximal _ this
+  refine ⟨_, Ideal.map_le_iff_le_comap.mp hM', hM.isPrime.comap _, ?_⟩
+  intro x hx
+  by_contra hx'
+  exact Set.disjoint_left.mp ((IsLocalization.isPrime_iff_isPrime_disjoint
+    (Algebra.algebraMapSubmonoid S P.primeCompl) Sₚ M).mp hM.isPrime).2 ⟨_, hx', rfl⟩ hx
+
+theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P : Ideal R) [IsPrime P]
+    (I : Ideal S) (hIP : I.comap (algebraMap R S) ≤ P) :
+    ∃ Q ≥ I, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
+  have ⟨P', hP, hP', hP''⟩ := exists_ideal_comap_le_prime P I hIP
+  obtain ⟨Q, hQ, hQ', hQ''⟩ := exists_ideal_over_prime_of_isIntegral_of_isPrime H P P' hP''
+  exact ⟨Q, hP.trans hQ, hQ', hQ''⟩
 #align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegral
 
 /-- `comap (algebraMap R S)` is a surjection from the max spec of `S` to max spec of `R`.
 `hP : (algebraMap R S).ker ≤ P` is a slight generalization of the extension being injective -/
-theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)
+theorem exists_ideal_over_maximal_of_isIntegral (H : Algebra.IsIntegral R S)
     (P : Ideal R) [P_max : IsMaximal P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsMaximal Q ∧ Q.comap (algebraMap R S) = P := by
-  obtain ⟨Q, ⟨Q_prime, hQ⟩⟩ := exists_ideal_over_prime_of_isIntegral' H P hP
+  obtain ⟨Q, -, Q_prime, hQ⟩ := exists_ideal_over_prime_of_isIntegral H P ⊥ hP
   exact ⟨Q, isMaximal_of_isIntegral_of_isMaximal_comap H _ (hQ.symm ▸ P_max), hQ⟩
 #align ideal.exists_ideal_over_maximal_of_is_integral Ideal.exists_ideal_over_maximal_of_isIntegral
 
+lemma map_eq_top_iff_of_ker_le
+    (f : R →+* S) {I : Ideal R} (hf₁ : RingHom.ker f ≤ I) (hf₂ : f.IsIntegral) :
+    I.map f = ⊤ ↔ I = ⊤ := by
+  constructor; swap
+  · rintro rfl; exact Ideal.map_top _
+  contrapose
+  intro h
+  obtain ⟨m, _, hm⟩ := Ideal.exists_le_maximal I h
+  letI := f.toAlgebra
+  obtain ⟨m', _, rfl⟩ := exists_ideal_over_maximal_of_isIntegral hf₂ m (hf₁.trans hm)
+  rw [← map_le_iff_le_comap] at hm
+  exact (hm.trans_lt (lt_top_iff_ne_top.mpr (IsMaximal.ne_top ‹_›))).ne
+
+lemma map_eq_top_iff
+    (f : R →+* S) {I : Ideal R} (hf₁ : Function.Injective f) (hf₂ : f.IsIntegral) :
+    I.map f = ⊤ ↔ I = ⊤ :=
+  map_eq_top_iff_of_ker_le f (by simp [f.injective_iff_ker_eq_bot.mp hf₁]) hf₂
+
 end IsDomain
 
 end Ideal

198cb64d

chore(IntegralClosure): noncommutative generalizations and golfs (#8406)

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.
Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit
Add a lemma Algebra.IsIntegral.of_injective.
Move isIntegral_of_(submodule_)noetherian down and golf them.
Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.
Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.
Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.
Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.
Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').
Combine isIntegral_trans_aux into isIntegral_trans and golf.
Add Algebra namespace to isIntegral_sup.
rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans
Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

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

8dba065d

Diff

@@ -269,7 +269,7 @@ theorem comap_ne_bot_of_algebraic_mem [IsDomain S] {x : S} (x_ne_zero : x ≠ 0)
 
 theorem comap_ne_bot_of_integral_mem [Nontrivial R] [IsDomain S] {x : S} (x_ne_zero : x ≠ 0)
     (x_mem : x ∈ I) (hx : IsIntegral R x) : I.comap (algebraMap R S) ≠ ⊥ :=
-  comap_ne_bot_of_algebraic_mem x_ne_zero x_mem (hx.isAlgebraic R)
+  comap_ne_bot_of_algebraic_mem x_ne_zero x_mem hx.isAlgebraic
 #align ideal.comap_ne_bot_of_integral_mem Ideal.comap_ne_bot_of_integral_mem
 
 theorem eq_bot_of_comap_eq_bot [Nontrivial R] [IsDomain S] (hRS : Algebra.IsIntegral R S)
@@ -284,9 +284,8 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
     [hI : I.IsMaximal] : IsMaximal (I.comap (algebraMap R S)) := by
   refine' Ideal.Quotient.maximal_of_isField _ _
   haveI : IsPrime (I.comap (algebraMap R S)) := comap_isPrime _ _
-  exact
-    isField_of_isIntegral_of_isField (Algebra.IsIntegral.quotient hRS)
-      algebraMap_quotient_injective (by rwa [← Quotient.maximal_ideal_iff_isField_quotient])
+  exact isField_of_isIntegral_of_isField hRS.quotient
+    algebraMap_quotient_injective (by rwa [← Quotient.maximal_ideal_iff_isField_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
 theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type*} [CommRing R] [CommRing S]
@@ -387,7 +386,7 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     ∃ Q ≥ I, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   obtain ⟨Q' : Ideal (S ⧸ I), ⟨Q'_prime, hQ'⟩⟩ :=
     @exists_ideal_over_prime_of_isIntegral' (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
-      Ideal.quotientAlgebra _ (Algebra.IsIntegral.quotient H)
+      Ideal.quotientAlgebra _ H.quotient
       (map (Ideal.Quotient.mk (I.comap (algebraMap R S))) P)
       (map_isPrime_of_surjective Quotient.mk_surjective (by simp [hIP]))
       (le_trans (le_of_eq ((RingHom.injective_iff_ker_eq_bot _).1 algebraMap_quotient_injective))

198cb64d

chore(RingTheory/{Algebraic, Localization/Integral}): rename decls to use dot notation (#8437)

This PR tests a string-based tool for renaming declarations.

Inspired by this Zulip thread, I am trying to reduce the diff of #8406.

This PR makes the following renames:

| From | To |

a76dc22f

Diff

@@ -285,7 +285,7 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
   refine' Ideal.Quotient.maximal_of_isField _ _
   haveI : IsPrime (I.comap (algebraMap R S)) := comap_isPrime _ _
   exact
-    isField_of_isIntegral_of_isField (isIntegral_quotient_of_isIntegral hRS)
+    isField_of_isIntegral_of_isField (Algebra.IsIntegral.quotient hRS)
       algebraMap_quotient_injective (by rwa [← Quotient.maximal_ideal_iff_isField_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
@@ -387,7 +387,7 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     ∃ Q ≥ I, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   obtain ⟨Q' : Ideal (S ⧸ I), ⟨Q'_prime, hQ'⟩⟩ :=
     @exists_ideal_over_prime_of_isIntegral' (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
-      Ideal.quotientAlgebra _ (isIntegral_quotient_of_isIntegral H)
+      Ideal.quotientAlgebra _ (Algebra.IsIntegral.quotient H)
       (map (Ideal.Quotient.mk (I.comap (algebraMap R S))) P)
       (map_isPrime_of_surjective Quotient.mk_surjective (by simp [hIP]))
       (le_trans (le_of_eq ((RingHom.injective_iff_ker_eq_bot _).1 algebraMap_quotient_injective))

198cb64d

chore: tidy various files (#7035)

d04897a6

Diff

@@ -150,13 +150,13 @@ theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S 
 #align ideal.comap_eq_of_scalar_tower_quotient Ideal.comap_eq_of_scalar_tower_quotient
 
 /-- If `P` lies over `p`, then `R / p` has a canonical map to `S / P`. -/
-def Quotient.algebraQuotientOfLeComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
+def Quotient.algebraQuotientOfLEComap (h : p ≤ comap f P) : Algebra (R ⧸ p) (S ⧸ P) :=
   RingHom.toAlgebra <| quotientMap _ f h
-#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLeComap
+#align ideal.quotient.algebra_quotient_of_le_comap Ideal.Quotient.algebraQuotientOfLEComap
 
 /-- `R / p` has a canonical map to `S / pS`. -/
 instance Quotient.algebraQuotientMapQuotient : Algebra (R ⧸ p) (S ⧸ map f p) :=
-  Ideal.Quotient.algebraQuotientOfLeComap le_comap_map
+  Ideal.Quotient.algebraQuotientOfLEComap le_comap_map
 #align ideal.quotient.algebra_quotient_map_quotient Ideal.Quotient.algebraQuotientMapQuotient
 
 @[simp]
@@ -236,13 +236,7 @@ theorem comap_lt_comap_of_integral_mem_sdiff [Algebra R S] [hI : I.IsPrime] (hIJ
     (mem : x ∈ (J : Set S) \ I) (integral : IsIntegral R x) :
     I.comap (algebraMap R S) < J.comap (algebraMap R S) := by
   obtain ⟨p, p_monic, hpx⟩ := integral
-  refine' comap_lt_comap_of_root_mem_sdiff hIJ mem _ _
-  swap
-  · apply map_monic_ne_zero p_monic
-    -- Porting note : no longer needed
-    -- apply Quotient.NonTrivial
-    -- apply mt comap_eq_top_iff.mp
-    -- apply hI.1
+  refine comap_lt_comap_of_root_mem_sdiff hIJ mem (map_monic_ne_zero p_monic) ?_
   convert I.zero_mem
 #align ideal.comap_lt_comap_of_integral_mem_sdiff Ideal.comap_lt_comap_of_integral_mem_sdiff

198cb64d

chore: tidy various files (#6577)

837c4ae2

Diff

@@ -139,11 +139,10 @@ then `P` lies over `p`.
 theorem comap_eq_of_scalar_tower_quotient [Algebra R S] [Algebra (R ⧸ p) (S ⧸ P)]
     [IsScalarTower R (R ⧸ p) (S ⧸ P)] (h : Function.Injective (algebraMap (R ⧸ p) (S ⧸ P))) :
     comap (algebraMap R S) P = p := by
-
-  ext x;
-  constructor <;>
-    rw [mem_comap, ← Quotient.eq_zero_iff_mem, ← Quotient.eq_zero_iff_mem, Quotient.mk_algebraMap,
-      IsScalarTower.algebraMap_apply R (R ⧸ p) (S ⧸ P), Quotient.algebraMap_eq]
+  ext x
+  rw [mem_comap, ← Quotient.eq_zero_iff_mem, ← Quotient.eq_zero_iff_mem, Quotient.mk_algebraMap,
+    IsScalarTower.algebraMap_apply R (R ⧸ p) (S ⧸ P), Quotient.algebraMap_eq]
+  constructor
   · intro hx
     exact (injective_iff_map_eq_zero (algebraMap (R ⧸ p) (S ⧸ P))).mp h _ hx
   · intro hx
@@ -361,7 +360,7 @@ theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integr
 
 /-- `comap (algebraMap R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
 `hP : (algebraMap R S).ker ≤ P` is a slight generalization of the extension being injective -/
-theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
+theorem exists_ideal_over_prime_of_isIntegral' (H : Algebra.IsIntegral R S) (P : Ideal R)
     [IsPrime P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   have hP0 : (0 : S) ∉ Algebra.algebraMapSubmonoid S P.primeCompl := by
@@ -382,24 +381,23 @@ theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P
     (M := P.primeCompl) (T := Algebra.algebraMapSubmonoid S P.primeCompl) (S := Rₚ) _
     _ _ _ _ _ (fun p hp => Algebra.mem_algebraMapSubmonoid_of_mem ⟨p, hp⟩) _ _]
   rfl
-#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_is_integral'
+#align ideal.exists_ideal_over_prime_of_is_integral' Ideal.exists_ideal_over_prime_of_isIntegral'
 
 end
 
-/-- More general going-up theorem than `exists_ideal_over_prime_of_is_integral'`.
+/-- More general going-up theorem than `exists_ideal_over_prime_of_isIntegral'`.
 TODO: Version of going-up theorem with arbitrary length chains (by induction on this)?
   Not sure how best to write an ascending chain in Lean -/
 theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P : Ideal R) [IsPrime P]
     (I : Ideal S) [IsPrime I] (hIP : I.comap (algebraMap R S) ≤ P) :
     ∃ Q ≥ I, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
   obtain ⟨Q' : Ideal (S ⧸ I), ⟨Q'_prime, hQ'⟩⟩ :=
-    @exists_ideal_over_prime_of_is_integral' (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
+    @exists_ideal_over_prime_of_isIntegral' (R ⧸ I.comap (algebraMap R S)) _ (S ⧸ I) _
       Ideal.quotientAlgebra _ (isIntegral_quotient_of_isIntegral H)
       (map (Ideal.Quotient.mk (I.comap (algebraMap R S))) P)
       (map_isPrime_of_surjective Quotient.mk_surjective (by simp [hIP]))
       (le_trans (le_of_eq ((RingHom.injective_iff_ker_eq_bot _).1 algebraMap_quotient_injective))
         bot_le)
-  haveI := Q'_prime
   refine' ⟨Q'.comap _, le_trans (le_of_eq mk_ker.symm) (ker_le_comap _), ⟨comap_isPrime _ Q', _⟩⟩
   rw [comap_comap]
   refine' _root_.trans _ (_root_.trans (congr_arg (comap (Ideal.Quotient.mk
@@ -415,8 +413,7 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
 theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)
     (P : Ideal R) [P_max : IsMaximal P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsMaximal Q ∧ Q.comap (algebraMap R S) = P := by
-  obtain ⟨Q, ⟨Q_prime, hQ⟩⟩ := exists_ideal_over_prime_of_is_integral' H P hP
-  haveI : Q.IsPrime := Q_prime
+  obtain ⟨Q, ⟨Q_prime, hQ⟩⟩ := exists_ideal_over_prime_of_isIntegral' H P hP
   exact ⟨Q, isMaximal_of_isIntegral_of_isMaximal_comap H _ (hQ.symm ▸ P_max), hQ⟩
 #align ideal.exists_ideal_over_maximal_of_is_integral Ideal.exists_ideal_over_maximal_of_isIntegral

198cb64d

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -27,7 +27,7 @@ can be proven using more general going-up/going-down theory.
 -/
 
 
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
 
 namespace Ideal
 
@@ -39,7 +39,7 @@ open Submodule
 
 section CommRing
 
-variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
+variable {S : Type*} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
 theorem coeff_zero_mem_comap_of_root_mem_of_eval_mem {r : S} (hr : r ∈ I) {p : R[X]}
     (hp : p.eval₂ f r ∈ I) : p.coeff 0 ∈ I.comap f := by
@@ -191,7 +191,7 @@ end CommRing
 
 section IsDomain
 
-variable {S : Type _} [CommRing S] {f : R →+* S} {I J : Ideal S}
+variable {S : Type*} [CommRing S] {f : R →+* S} {I J : Ideal S}
 
 theorem exists_coeff_ne_zero_mem_comap_of_root_mem [IsDomain S] {r : S} (r_ne_zero : r ≠ 0)
     (hr : r ∈ I) {p : R[X]} :
@@ -296,14 +296,14 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
       algebraMap_quotient_injective (by rwa [← Quotient.maximal_ideal_iff_isField_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
-theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type _} [CommRing R] [CommRing S]
+theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type*} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_isMaximal'
 
 section IsIntegralClosure
 
-variable (S) {A : Type _} [CommRing A]
+variable (S) {A : Type*} [CommRing A]
 
 variable [Algebra R A] [Algebra A S] [IsScalarTower R A S] [IsIntegralClosure A R S]

198cb64d

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.ideal.over
-! leanprover-community/mathlib commit 198cb64d5c961e1a8d0d3e219feb7058d5353861
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Algebraic
 import Mathlib.RingTheory.Localization.AtPrime
 import Mathlib.RingTheory.Localization.Integral
 
+#align_import ring_theory.ideal.over from "leanprover-community/mathlib"@"198cb64d5c961e1a8d0d3e219feb7058d5353861"
+
 /-!
 # Ideals over/under ideals

198cb64d

fix: filenames with typos in doc (#5836)

1657aebc

Diff

@@ -99,7 +99,7 @@ theorem injective_quotient_le_comap_map (P : Ideal R[X]) :
 R[x] / P → (R / (P ∩ R))[x] / (P / (P ∩ R))
 ```
 commutes.  It is used, for instance, in the proof of `quotient_mk_comp_C_is_integral_of_jacobson`,
-in the file `ring_theory/jacobson`.
+in the file `RingTheory.Jacobson`.
 -/
 theorem quotient_mk_maps_eq (P : Ideal R[X]) :
     ((Quotient.mk (map (mapRingHom (Quotient.mk (P.comap (C : R →+* R[X])))) P)).comp C).comp

198cb64d

chore: fix focusing dots (#5708)

This PR is the result of running

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

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

cb02d09e

Diff

@@ -69,8 +69,8 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     rw [eval₂_mul, eval₂_X] at hp
     obtain ⟨i, hi, mem⟩ := ih p_nonzero (r_non_zero_divisor hp)
     refine' ⟨i + 1, _, _⟩
-    . simp [hi, mem]
-    . simpa [hi] using mem
+    · simp [hi, mem]
+    · simpa [hi] using mem
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
 
 /-- Let `P` be an ideal in `R[x]`.  The map

198cb64d

feat: port RingTheory.Jacobson (#4338)

Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

9b91d86c

Diff

@@ -299,10 +299,10 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
       algebraMap_quotient_injective (by rwa [← Quotient.maximal_ideal_iff_isField_quotient])
 #align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
 
-theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
+theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type _} [CommRing R] [CommRing S]
     (f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
   @isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
-#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'
+#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_isMaximal'
 
 section IsIntegralClosure

198cb64d

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -362,8 +362,8 @@ theorem IntegralClosure.eq_bot_of_comap_eq_bot [Nontrivial R] {I : Ideal (integr
   IsIntegralClosure.eq_bot_of_comap_eq_bot S
 #align ideal.integral_closure.eq_bot_of_comap_eq_bot Ideal.IntegralClosure.eq_bot_of_comap_eq_bot
 
-/-- `comap (algebra_map R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
-`hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
+/-- `comap (algebraMap R S)` is a surjection from the prime spec of `R` to prime spec of `S`.
+`hP : (algebraMap R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_prime_of_is_integral' (H : Algebra.IsIntegral R S) (P : Ideal R)
     [IsPrime P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsPrime Q ∧ Q.comap (algebraMap R S) = P := by
@@ -413,8 +413,8 @@ theorem exists_ideal_over_prime_of_isIntegral (H : Algebra.IsIntegral R S) (P :
     simpa [← RingHom.ker_eq_comap_bot] using hIP
 #align ideal.exists_ideal_over_prime_of_is_integral Ideal.exists_ideal_over_prime_of_isIntegral
 
-/-- `comap (algebra_map R S)` is a surjection from the max spec of `S` to max spec of `R`.
-`hP : (algebra_map R S).ker ≤ P` is a slight generalization of the extension being injective -/
+/-- `comap (algebraMap R S)` is a surjection from the max spec of `S` to max spec of `R`.
+`hP : (algebraMap R S).ker ≤ P` is a slight generalization of the extension being injective -/
 theorem exists_ideal_over_maximal_of_isIntegral [IsDomain S] (H : Algebra.IsIntegral R S)
     (P : Ideal R) [P_max : IsMaximal P] (hP : RingHom.ker (algebraMap R S) ≤ P) :
     ∃ Q : Ideal S, IsMaximal Q ∧ Q.comap (algebraMap R S) = P := by

198cb64d

feat: port RingTheory.Ideal.Over (#4270)

f1455f1d

`ring_theory.ideal.over` ⟷ `Mathlib.RingTheory.Ideal.Over`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 633

ring_theory.ideal.over ⟷ Mathlib.RingTheory.Ideal.Over

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 633

`ring_theory.ideal.over` ⟷ `Mathlib.RingTheory.Ideal.Over`