ring_theory.localization.ideal ⟷ Mathlib.RingTheory.Localization.Ideal

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

@@ -130,17 +130,17 @@ theorem isPrime_iff_isPrime_disjoint (J : Ideal S) :
       rw [eq_top_iff, ← (OrderEmbedding M S).le_iff_le]
       exact le_of_eq hJ.symm
     · intro x y hxy
-      rw [Ideal.mem_comap, RingHom.map_mul] at hxy 
+      rw [Ideal.mem_comap, RingHom.map_mul] at hxy
       exact h.mem_or_mem hxy
   · refine' fun h => ⟨fun hJ => h.left.ne_top (eq_top_iff.2 _), _⟩
-    · rwa [eq_top_iff, ← (OrderEmbedding M S).le_iff_le] at hJ 
+    · rwa [eq_top_iff, ← (OrderEmbedding M S).le_iff_le] at hJ
     · intro x y hxy
       obtain ⟨a, s, ha⟩ := mk'_surjective M x
       obtain ⟨b, t, hb⟩ := mk'_surjective M y
       have : mk' S (a * b) (s * t) ∈ J := by rwa [mk'_mul, ha, hb]
-      rw [mk'_mem_iff, ← Ideal.mem_comap] at this 
+      rw [mk'_mem_iff, ← Ideal.mem_comap] at this
       replace this := h.left.mem_or_mem this
-      rw [Ideal.mem_comap, Ideal.mem_comap] at this 
+      rw [Ideal.mem_comap, Ideal.mem_comap] at this
       rwa [← ha, ← hb, mk'_mem_iff, mk'_mem_iff]
 #align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjoint
 -/
@@ -197,18 +197,18 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
   by_cases hM : (Ideal.Quotient.mk (I.comap (algebraMap R S))) m = 0
   · have : I = ⊤ := by
       rw [Ideal.eq_top_iff_one]
-      rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_comap] at hM 
+      rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_comap] at hM
       convert I.mul_mem_right (mk' S (1 : R) ⟨m, hm⟩) hM
       rw [← mk'_eq_mul_mk'_one, mk'_self]
     exact ⟨0, eq_comm.1 (by simp [Ideal.Quotient.eq_zero_iff_mem, this])⟩
-  · rw [Ideal.Quotient.maximal_ideal_iff_isField_quotient] at hI 
+  · rw [Ideal.Quotient.maximal_ideal_iff_isField_quotient] at hI
     obtain ⟨n, hn⟩ := hI.3 hM
     obtain ⟨rn, rfl⟩ := Ideal.Quotient.mk_surjective n
     refine' ⟨(Ideal.Quotient.mk J) (r * rn), _⟩
     -- The rest of the proof is essentially just algebraic manipulations to prove the equality
-    rw [← RingHom.map_mul] at hn 
+    rw [← RingHom.map_mul] at hn
     replace hn := congr_arg (Ideal.quotientMap I (algebraMap R S) le_rfl) hn
-    simp only [RingHom.map_one, Ideal.quotientMap_mk, RingHom.map_mul] at hn 
+    simp only [RingHom.map_one, Ideal.quotientMap_mk, RingHom.map_mul] at hn
     rw [Ideal.quotientMap_mk, ← sub_eq_zero, ← RingHom.map_sub, Ideal.Quotient.eq_zero_iff_mem, ←
       Ideal.Quotient.eq_zero_iff_mem, RingHom.map_sub, sub_eq_zero, mk'_eq_mul_mk'_one]
     simp only [mul_eq_mul_left_iff, RingHom.map_mul]

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

@@ -3,8 +3,8 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 -/
-import Mathbin.RingTheory.Ideal.QuotientOperations
-import Mathbin.RingTheory.Localization.Basic
+import RingTheory.Ideal.QuotientOperations
+import RingTheory.Localization.Basic
 
 #align_import ring_theory.localization.ideal from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -42,7 +42,7 @@ private def map_ideal (I : Ideal R) : Ideal S
   zero_mem' := ⟨⟨0, 1⟩, by simp⟩
   add_mem' := by
     rintro a b ⟨a', ha⟩ ⟨b', hb⟩
-    use ⟨a'.2 * b'.1 + b'.2 * a'.1, I.add_mem (I.mul_mem_left _ b'.1.2) (I.mul_mem_left _ a'.1.2)⟩
+    use⟨a'.2 * b'.1 + b'.2 * a'.1, I.add_mem (I.mul_mem_left _ b'.1.2) (I.mul_mem_left _ a'.1.2)⟩
     use a'.2 * b'.2
     simp only [RingHom.map_add, Submodule.coe_mk, Submonoid.coe_mul, RingHom.map_mul]
     rw [add_mul, ← mul_assoc a, ha, mul_comm (algebraMap R S a'.2) (algebraMap R S b'.2), ←
@@ -51,7 +51,7 @@ private def map_ideal (I : Ideal R) : Ideal S
   smul_mem' := by
     rintro c x ⟨x', hx⟩
     obtain ⟨c', hc⟩ := IsLocalization.surj M c
-    use ⟨c'.1 * x'.1, I.mul_mem_left c'.1 x'.1.2⟩
+    use⟨c'.1 * x'.1, I.mul_mem_left c'.1 x'.1.2⟩
     use c'.2 * x'.2
     simp only [← hx, ← hc, smul_eq_mul, Submodule.coe_mk, Submonoid.coe_mul, RingHom.map_mul]
     ring
@@ -64,7 +64,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
   · change _ → z ∈ map_ideal M S I
     refine' fun h => Ideal.mem_sInf.1 h fun z hz => _
     obtain ⟨y, hy⟩ := hz
-    use ⟨⟨⟨y, hy.left⟩, 1⟩, by simp [hy.right]⟩
+    use⟨⟨⟨y, hy.left⟩, 1⟩, by simp [hy.right]⟩
   · rintro ⟨⟨a, s⟩, h⟩
     rw [← Ideal.unit_mul_mem_iff_mem _ (map_units S s), mul_comm]
     exact h.symm ▸ Ideal.mem_map_of_mem _ a.2

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

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.ideal
-! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Ideal.QuotientOperations
 import Mathbin.RingTheory.Localization.Basic
 
+#align_import ring_theory.localization.ideal from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
+
 /-!
 # Ideals in localizations of commutative rings
 

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

@@ -35,8 +35,6 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 
 variable [Algebra R S] [IsLocalization M S]
 
-include M
-
 /-- Explicit characterization of the ideal given by `ideal.map (algebra_map R S) I`.
 In practice, this ideal differs only in that the carrier set is defined explicitly.
 This definition is only meant to be used in proving `mem_map_algebra_map_iff`,
@@ -61,6 +59,7 @@ private def map_ideal (I : Ideal R) : Ideal S
     simp only [← hx, ← hc, smul_eq_mul, Submodule.coe_mk, Submonoid.coe_mul, RingHom.map_mul]
     ring
 
+#print IsLocalization.mem_map_algebraMap_iff /-
 theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
   by
@@ -73,6 +72,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     rw [← Ideal.unit_mul_mem_iff_mem _ (map_units S s), mul_comm]
     exact h.symm ▸ Ideal.mem_map_of_mem _ a.2
 #align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iff
+-/
 
 #print IsLocalization.map_comap /-
 theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algebraMap R S) J) = J :=
@@ -88,6 +88,7 @@ theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algeb
 #align is_localization.map_comap IsLocalization.map_comap
 -/
 
+#print IsLocalization.comap_map_of_isPrime_disjoint /-
 theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjoint (M : Set R) I) :
     Ideal.comap (algebraMap R S) (Ideal.map (algebraMap R S) I) = I :=
   by
@@ -99,6 +100,7 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   have : ↑c * ↑s * a ∈ I := by rw [mul_assoc, hc]; exact I.mul_mem_left c b.2
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
+-/
 
 #print IsLocalization.orderEmbedding /-
 /-- If `S` is the localization of `R` at a submonoid, the ordering of ideals of `S` is
@@ -112,6 +114,7 @@ def orderEmbedding : Ideal S ↪o Ideal R
 #align is_localization.order_embedding IsLocalization.orderEmbedding
 -/
 
+#print IsLocalization.isPrime_iff_isPrime_disjoint /-
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its comap,
@@ -143,7 +146,9 @@ theorem isPrime_iff_isPrime_disjoint (J : Ideal S) :
       rw [Ideal.mem_comap, Ideal.mem_comap] at this 
       rwa [← ha, ← hb, mk'_mem_iff, mk'_mem_iff]
 #align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjoint
+-/
 
+#print IsLocalization.isPrime_of_isPrime_disjoint /-
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its map,
@@ -154,7 +159,9 @@ theorem isPrime_of_isPrime_disjoint (I : Ideal R) (hp : I.IsPrime) (hd : Disjoin
   rw [is_prime_iff_is_prime_disjoint M S, comap_map_of_is_prime_disjoint M S I hp hd]
   exact ⟨hp, hd⟩
 #align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjoint
+-/
 
+#print IsLocalization.orderIsoOfPrime /-
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M` -/
 def orderIsoOfPrime :
@@ -169,6 +176,7 @@ def orderIsoOfPrime :
       show I.val ≤ I'.val from map_comap M S I.val ▸ map_comap M S I'.val ▸ Ideal.map_mono h,
       fun h x hx => h hx⟩
 #align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrime
+-/
 
 end CommSemiring
 
@@ -178,8 +186,7 @@ variable {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
 
 variable [Algebra R S] [IsLocalization M S]
 
-include M
-
+#print IsLocalization.surjective_quotientMap_of_maximal_of_localization /-
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
   and the localization necessarily maps the equivalence class of the inverse in the localization -/
@@ -217,9 +224,11 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
                 (Ideal.mem_comap.2 (Ideal.Quotient.eq_zero_iff_mem.1 hn))))
           (trans hn (by rw [← RingHom.map_mul, ← mk'_eq_mul_mk'_one, mk'_self, RingHom.map_one])))
 #align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localization
+-/
 
 open scoped nonZeroDivisors
 
+#print IsLocalization.bot_lt_comap_prime /-
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=
   by
@@ -229,6 +238,7 @@ theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p
       (show (⟨⊥, Ideal.bot_prime⟩ : { p : Ideal S // p.IsPrime }) < ⟨p, hpp⟩ from hp0.bot_lt)
   exact (Ideal.comap_bot_of_injective (algebraMap R S) (IsLocalization.injective _ hM)).symm
 #align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_prime
+-/
 
 end CommRing
 

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

@@ -43,7 +43,7 @@ This definition is only meant to be used in proving `mem_map_algebra_map_iff`,
 and any proof that needs to refer to the explicit carrier set should use that theorem. -/
 private def map_ideal (I : Ideal R) : Ideal S
     where
-  carrier := { z : S | ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 }
+  carrier := {z : S | ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1}
   zero_mem' := ⟨⟨0, 1⟩, by simp⟩
   add_mem' := by
     rintro a b ⟨a', ha⟩ ⟨b', hb⟩
@@ -224,7 +224,8 @@ theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=
   by
   haveI : IsDomain S := is_domain_of_le_non_zero_divisors _ hM
-  convert(order_iso_of_prime M S).lt_iff_lt.mpr
+  convert
+    (order_iso_of_prime M S).lt_iff_lt.mpr
       (show (⟨⊥, Ideal.bot_prime⟩ : { p : Ideal S // p.IsPrime }) < ⟨p, hpp⟩ from hp0.bot_lt)
   exact (Ideal.comap_bot_of_injective (algebraMap R S) (IsLocalization.injective _ hM)).symm
 #align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_prime

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

@@ -79,7 +79,7 @@ theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algeb
   le_antisymm (Ideal.map_le_iff_le_comap.2 le_rfl) fun x hJ =>
     by
     obtain ⟨r, s, hx⟩ := mk'_surjective M x
-    rw [← hx] at hJ⊢
+    rw [← hx] at hJ ⊢
     exact
       Ideal.mul_mem_right _ _
         (Ideal.mem_map_of_mem _
@@ -130,17 +130,17 @@ theorem isPrime_iff_isPrime_disjoint (J : Ideal S) :
       rw [eq_top_iff, ← (OrderEmbedding M S).le_iff_le]
       exact le_of_eq hJ.symm
     · intro x y hxy
-      rw [Ideal.mem_comap, RingHom.map_mul] at hxy
+      rw [Ideal.mem_comap, RingHom.map_mul] at hxy 
       exact h.mem_or_mem hxy
   · refine' fun h => ⟨fun hJ => h.left.ne_top (eq_top_iff.2 _), _⟩
-    · rwa [eq_top_iff, ← (OrderEmbedding M S).le_iff_le] at hJ
+    · rwa [eq_top_iff, ← (OrderEmbedding M S).le_iff_le] at hJ 
     · intro x y hxy
       obtain ⟨a, s, ha⟩ := mk'_surjective M x
       obtain ⟨b, t, hb⟩ := mk'_surjective M y
       have : mk' S (a * b) (s * t) ∈ J := by rwa [mk'_mul, ha, hb]
-      rw [mk'_mem_iff, ← Ideal.mem_comap] at this
+      rw [mk'_mem_iff, ← Ideal.mem_comap] at this 
       replace this := h.left.mem_or_mem this
-      rw [Ideal.mem_comap, Ideal.mem_comap] at this
+      rw [Ideal.mem_comap, Ideal.mem_comap] at this 
       rwa [← ha, ← hb, mk'_mem_iff, mk'_mem_iff]
 #align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjoint
 
@@ -193,18 +193,18 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
   by_cases hM : (Ideal.Quotient.mk (I.comap (algebraMap R S))) m = 0
   · have : I = ⊤ := by
       rw [Ideal.eq_top_iff_one]
-      rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_comap] at hM
+      rw [Ideal.Quotient.eq_zero_iff_mem, Ideal.mem_comap] at hM 
       convert I.mul_mem_right (mk' S (1 : R) ⟨m, hm⟩) hM
       rw [← mk'_eq_mul_mk'_one, mk'_self]
     exact ⟨0, eq_comm.1 (by simp [Ideal.Quotient.eq_zero_iff_mem, this])⟩
-  · rw [Ideal.Quotient.maximal_ideal_iff_isField_quotient] at hI
+  · rw [Ideal.Quotient.maximal_ideal_iff_isField_quotient] at hI 
     obtain ⟨n, hn⟩ := hI.3 hM
     obtain ⟨rn, rfl⟩ := Ideal.Quotient.mk_surjective n
     refine' ⟨(Ideal.Quotient.mk J) (r * rn), _⟩
     -- The rest of the proof is essentially just algebraic manipulations to prove the equality
-    rw [← RingHom.map_mul] at hn
+    rw [← RingHom.map_mul] at hn 
     replace hn := congr_arg (Ideal.quotientMap I (algebraMap R S) le_rfl) hn
-    simp only [RingHom.map_one, Ideal.quotientMap_mk, RingHom.map_mul] at hn
+    simp only [RingHom.map_one, Ideal.quotientMap_mk, RingHom.map_mul] at hn 
     rw [Ideal.quotientMap_mk, ← sub_eq_zero, ← RingHom.map_sub, Ideal.Quotient.eq_zero_iff_mem, ←
       Ideal.Quotient.eq_zero_iff_mem, RingHom.map_sub, sub_eq_zero, mk'_eq_mul_mk'_one]
     simp only [mul_eq_mul_left_iff, RingHom.map_mul]

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

@@ -100,6 +100,7 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
 
+#print IsLocalization.orderEmbedding /-
 /-- If `S` is the localization of `R` at a submonoid, the ordering of ideals of `S` is
 embedded in the ordering of ideals of `R`. -/
 def orderEmbedding : Ideal S ↪o Ideal R
@@ -109,6 +110,7 @@ def orderEmbedding : Ideal S ↪o Ideal R
   map_rel_iff' J₁ J₂ :=
     ⟨fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ, Ideal.comap_mono⟩
 #align is_localization.order_embedding IsLocalization.orderEmbedding
+-/
 
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
@@ -216,7 +218,7 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
           (trans hn (by rw [← RingHom.map_mul, ← mk'_eq_mul_mk'_one, mk'_self, RingHom.map_one])))
 #align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localization
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=

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

@@ -61,9 +61,6 @@ private def map_ideal (I : Ideal R) : Ideal S
     simp only [← hx, ← hc, smul_eq_mul, Submodule.coe_mk, Submonoid.coe_mul, RingHom.map_mul]
     ring
 
-/- warning: is_localization.mem_map_algebra_map_iff -> IsLocalization.mem_map_algebraMap_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iffₓ'. -/
 theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
   by
@@ -91,12 +88,6 @@ theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algeb
 #align is_localization.map_comap IsLocalization.map_comap
 -/
 
-/- warning: is_localization.comap_map_of_is_prime_disjoint -> IsLocalization.comap_map_of_isPrime_disjoint is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjointₓ'. -/
 theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjoint (M : Set R) I) :
     Ideal.comap (algebraMap R S) (Ideal.map (algebraMap R S) I) = I :=
   by
@@ -109,12 +100,6 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.order_embedding IsLocalization.orderEmbeddingₓ'. -/
 /-- If `S` is the localization of `R` at a submonoid, the ordering of ideals of `S` is
 embedded in the ordering of ideals of `R`. -/
 def orderEmbedding : Ideal S ↪o Ideal R
@@ -125,12 +110,6 @@ def orderEmbedding : Ideal S ↪o Ideal R
     ⟨fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ, Ideal.comap_mono⟩
 #align is_localization.order_embedding IsLocalization.orderEmbedding
 
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-Case conversion may be inaccurate. Consider using '#align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjointₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its comap,
@@ -163,12 +142,6 @@ theorem isPrime_iff_isPrime_disjoint (J : Ideal S) :
       rwa [← ha, ← hb, mk'_mem_iff, mk'_mem_iff]
 #align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjoint
 
-/- warning: is_localization.is_prime_of_is_prime_disjoint -> IsLocalization.isPrime_of_isPrime_disjoint is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjointₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its map,
@@ -180,9 +153,6 @@ theorem isPrime_of_isPrime_disjoint (I : Ideal R) (hp : I.IsPrime) (hd : Disjoin
   exact ⟨hp, hd⟩
 #align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjoint
 
-/- warning: is_localization.order_iso_of_prime -> IsLocalization.orderIsoOfPrime is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrimeₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M` -/
 def orderIsoOfPrime :
@@ -208,9 +178,6 @@ variable [Algebra R S] [IsLocalization M S]
 
 include M
 
-/- warning: is_localization.surjective_quotient_map_of_maximal_of_localization -> IsLocalization.surjective_quotientMap_of_maximal_of_localization is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
   and the localization necessarily maps the equivalence class of the inverse in the localization -/
@@ -251,9 +218,6 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
 
 open nonZeroDivisors
 
-/- warning: is_localization.bot_lt_comap_prime -> IsLocalization.bot_lt_comap_prime is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_primeₓ'. -/
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=
   by

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

@@ -105,9 +105,7 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   replace h : algebraMap R S (s * a) = algebraMap R S b := by
     simpa only [← map_mul, mul_comm] using h
   obtain ⟨c, hc⟩ := (eq_iff_exists M S).1 h
-  have : ↑c * ↑s * a ∈ I := by
-    rw [mul_assoc, hc]
-    exact I.mul_mem_left c b.2
+  have : ↑c * ↑s * a ∈ I := by rw [mul_assoc, hc]; exact I.mul_mem_left c b.2
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
 

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

@@ -60,13 +60,9 @@ private def map_ideal (I : Ideal R) : Ideal S
     use c'.2 * x'.2
     simp only [← hx, ← hc, smul_eq_mul, Submodule.coe_mk, Submonoid.coe_mul, RingHom.map_mul]
     ring
-#align is_localization.map_ideal is_localization.map_ideal
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iffₓ'. -/
 theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
@@ -187,10 +183,7 @@ theorem isPrime_of_isPrime_disjoint (I : Ideal R) (hp : I.IsPrime) (hd : Disjoin
 #align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjoint
 
 /- warning: is_localization.order_iso_of_prime -> IsLocalization.orderIsoOfPrime is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrimeₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M` -/
@@ -218,10 +211,7 @@ variable [Algebra R S] [IsLocalization M S]
 include M
 
 /- warning: is_localization.surjective_quotient_map_of_maximal_of_localization -> IsLocalization.surjective_quotientMap_of_maximal_of_localization is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
@@ -264,10 +254,7 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
 open nonZeroDivisors
 
 /- warning: is_localization.bot_lt_comap_prime -> IsLocalization.bot_lt_comap_prime is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R 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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) M (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (p : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hpp : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p], (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) p (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)))))) -> (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)))))))) (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))))) (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) p)))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (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 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall (p : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [hpp : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) p], (Ne.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) p (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)))))) -> (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)))))))) (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))))) (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)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_primeₓ'. -/
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=

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

@@ -66,7 +66,7 @@ private def map_ideal (I : Ideal R) : Ideal S
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {z : S}, Iff (Membership.Mem.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (SetLike.hasMem.{u2, u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) S (Submodule.setLike.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) z (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) I)) (Exists.{succ u1} (Prod.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) I) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M)) (fun (x : Prod.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) I) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) M)) => Eq.{succ u2} S (HMul.hMul.{u2, u2, 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 but is expected to have type
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x))) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) I)) (Prod.fst.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R 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+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_4 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)} {z : S}, Iff (Membership.mem.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) S (Submodule.setLike.{u1, u1} S S (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) z (Ideal.map.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) I)) (Exists.{succ u2} (Prod.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) x I)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x M))) (fun (x : Prod.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) x I)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x M))) => Eq.{succ u1} S (HMul.hMul.{u1, u1, u1} S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) M)) (Prod.snd.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) x I)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x M)) x))) S (instHMul.{u1} S (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) M)) (Prod.snd.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x M)) x)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Subtype.val.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Set.{u2} R) (Set.instMembershipSet.{u2} R) x (SetLike.coe.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) I)) (Prod.fst.{u2, u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) x I)) (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) x M)) x)))))
 Case conversion may be inaccurate. Consider using '#align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iffₓ'. -/
 theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
@@ -221,7 +221,7 @@ include M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : 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)))))))) J (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)}, (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)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S 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_inst_2) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I)) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_5 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I] {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J (Ideal.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) 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 (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) I)) -> (Function.Surjective.{succ u1, succ 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) J) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (fun (_x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) I) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) H)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_5 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I] {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J (Ideal.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) 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 (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) I)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R 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(Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (fun (_x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) I) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) H)))
 Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,

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

@@ -115,7 +115,12 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
 
-#print IsLocalization.orderEmbedding /-
+/- warning: is_localization.order_embedding -> IsLocalization.orderEmbedding is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], OrderEmbedding.{u2, u1} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], OrderEmbedding.{u2, u1} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align is_localization.order_embedding IsLocalization.orderEmbeddingₓ'. -/
 /-- If `S` is the localization of `R` at a submonoid, the ordering of ideals of `S` is
 embedded in the ordering of ideals of `R`. -/
 def orderEmbedding : Ideal S ↪o Ideal R
@@ -125,7 +130,6 @@ def orderEmbedding : Ideal S ↪o Ideal R
   map_rel_iff' J₁ J₂ :=
     ⟨fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ, Ideal.comap_mono⟩
 #align is_localization.order_embedding IsLocalization.orderEmbedding
--/
 
 /- warning: is_localization.is_prime_iff_is_prime_disjoint -> IsLocalization.isPrime_iff_isPrime_disjoint is a dubious translation:
 lean 3 declaration is
@@ -184,7 +188,7 @@ theorem isPrime_of_isPrime_disjoint (I : Ideal R) (hp : I.IsPrime) (hd : Disjoin
 
 /- warning: is_localization.order_iso_of_prime -> IsLocalization.orderIsoOfPrime is a dubious translation:
 lean 3 declaration is
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(Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.completeBooleanAlgebra.{u1} R)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} R) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{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) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], OrderIso.{u2, u1} (Subtype.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) 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(CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) p)))) (Subtype.hasLe.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Preorder.toHasLe.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.hasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.completeBooleanAlgebra.{u1} R)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} R) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{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) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) p))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], OrderIso.{u2, u1} (Subtype.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} R) (Preorder.toLE.{u1} (Set.{u1} R) (PartialOrder.toPreorder.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) M) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)))) (Subtype.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} R) (Preorder.toLE.{u1} (Set.{u1} R) (PartialOrder.toPreorder.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) M) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p))))
 Case conversion may be inaccurate. Consider using '#align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrimeₓ'. -/
@@ -215,7 +219,7 @@ include M
 
 /- warning: is_localization.surjective_quotient_map_of_maximal_of_localization -> IsLocalization.surjective_quotientMap_of_maximal_of_localization is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toLE.{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)))))))) J (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)}, (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)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I)) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : 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)))))))) J (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)}, (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)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I)) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_5 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I] {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J (Ideal.comap.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) I) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) H)))
 Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
@@ -261,7 +265,7 @@ open nonZeroDivisors
 
 /- warning: is_localization.bot_lt_comap_prime -> IsLocalization.bot_lt_comap_prime is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) M (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (p : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hpp : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p], (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) p (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)))))) -> (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))) (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)))))))) (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))))) (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) p)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) M (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (p : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hpp : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p], (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) p (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)))))) -> (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)))))))) (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))))) (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) p)))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (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 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall (p : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [hpp : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) p], (Ne.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) p (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)))))) -> (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)))))))) (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))))) (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)))
 Case conversion may be inaccurate. Consider using '#align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_primeₓ'. -/

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

@@ -73,7 +73,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
   by
   constructor
   · change _ → z ∈ map_ideal M S I
-    refine' fun h => Ideal.mem_infₛ.1 h fun z hz => _
+    refine' fun h => Ideal.mem_sInf.1 h fun z hz => _
     obtain ⟨y, hy⟩ := hz
     use ⟨⟨⟨y, hy.left⟩, 1⟩, by simp [hy.right]⟩
   · rintro ⟨⟨a, s⟩, h⟩

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

@@ -217,7 +217,7 @@ include M
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toLE.{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)))))))) J (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)}, (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)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I)) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toLE.{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))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))))) J (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.instRingHomClassRingHom.{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.{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.instRingHomClassRingHom.{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)) -> (Function.Surjective.{succ u1, succ u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (fun (_x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) => HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))))) (NonUnitalNonAssocSemiring.toMul.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))} [_inst_5 : Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) I] {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) J (Ideal.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) 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 (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) I)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (fun (_x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) => HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{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) I) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R _inst_1) J) (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) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{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) I) (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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) _inst_3) H)))
 Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
@@ -263,7 +263,7 @@ open nonZeroDivisors
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) M (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (p : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hpp : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p], (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) p (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)))))) -> (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))) (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)))))))) (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))))) (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) p)))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_4 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall (p : Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) [hpp : Ideal.IsPrime.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) p], (Ne.{succ u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) p (Bot.bot.{u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Submodule.instBotSubmodule.{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)))))) -> (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)))))))) (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))))) (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 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{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 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) p)))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (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 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall (p : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) [hpp : Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) p], (Ne.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) p (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)))))) -> (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)))))))) (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))))) (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)))
 Case conversion may be inaccurate. Consider using '#align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_primeₓ'. -/
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.localization.ideal
-! leanprover-community/mathlib commit e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74
+! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Localization.Basic
 /-!
 # Ideals in localizations of commutative rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Implementation notes
 
 See `src/ring_theory/localization/basic.lean` for a design overview.

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

@@ -59,6 +59,12 @@ private def map_ideal (I : Ideal R) : Ideal S
     ring
 #align is_localization.map_ideal is_localization.map_ideal
 
+/- warning: is_localization.mem_map_algebra_map_iff -> IsLocalization.mem_map_algebraMap_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iffₓ'. -/
 theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
   by
@@ -72,6 +78,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
     exact h.symm ▸ Ideal.mem_map_of_mem _ a.2
 #align is_localization.mem_map_algebra_map_iff IsLocalization.mem_map_algebraMap_iff
 
+#print IsLocalization.map_comap /-
 theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algebraMap R S) J) = J :=
   le_antisymm (Ideal.map_le_iff_le_comap.2 le_rfl) fun x hJ =>
     by
@@ -83,7 +90,14 @@ theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algeb
           (show (algebraMap R S) r ∈ J from
             mk'_spec S r s ▸ J.mul_mem_right ((algebraMap R S) s) hJ))
 #align is_localization.map_comap IsLocalization.map_comap
+-/
 
+/- warning: is_localization.comap_map_of_is_prime_disjoint -> IsLocalization.comap_map_of_isPrime_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I) -> (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.completeBooleanAlgebra.{u1} R)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} R) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{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) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) I)) -> (Eq.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) I)) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_4 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), (Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) I) -> (Disjoint.{u2} (Set.{u2} R) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} R) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} R) (Preorder.toLE.{u2} (Set.{u2} R) (PartialOrder.toPreorder.{u2} (Set.{u2} R) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} R) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))) (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) M) (SetLike.coe.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) I)) -> (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) (Ideal.map.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) I)) I)
+Case conversion may be inaccurate. Consider using '#align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjointₓ'. -/
 theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjoint (M : Set R) I) :
     Ideal.comap (algebraMap R S) (Ideal.map (algebraMap R S) I) = I :=
   by
@@ -98,6 +112,7 @@ theorem comap_map_of_isPrime_disjoint (I : Ideal R) (hI : I.IsPrime) (hM : Disjo
   exact (hI.mem_or_mem this).resolve_left fun hsc => hM.le_bot ⟨(c * s).2, hsc⟩
 #align is_localization.comap_map_of_is_prime_disjoint IsLocalization.comap_map_of_isPrime_disjoint
 
+#print IsLocalization.orderEmbedding /-
 /-- If `S` is the localization of `R` at a submonoid, the ordering of ideals of `S` is
 embedded in the ordering of ideals of `R`. -/
 def orderEmbedding : Ideal S ↪o Ideal R
@@ -107,7 +122,14 @@ def orderEmbedding : Ideal S ↪o Ideal R
   map_rel_iff' J₁ J₂ :=
     ⟨fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ, Ideal.comap_mono⟩
 #align is_localization.order_embedding IsLocalization.orderEmbedding
+-/
 
+/- warning: is_localization.is_prime_iff_is_prime_disjoint -> IsLocalization.isPrime_iff_isPrime_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)), Iff (Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) J) (And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) J)) (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.completeBooleanAlgebra.{u1} R)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} R) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{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) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) J))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (J : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)), Iff (Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) J) (And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) J)) (Disjoint.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} R) (Preorder.toLE.{u1} (Set.{u1} R) (PartialOrder.toPreorder.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) M) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{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 _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) J))))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjointₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its comap,
@@ -140,6 +162,12 @@ theorem isPrime_iff_isPrime_disjoint (J : Ideal S) :
       rwa [← ha, ← hb, mk'_mem_iff, mk'_mem_iff]
 #align is_localization.is_prime_iff_is_prime_disjoint IsLocalization.isPrime_iff_isPrime_disjoint
 
+/- warning: is_localization.is_prime_of_is_prime_disjoint -> IsLocalization.isPrime_of_isPrime_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I) -> (Disjoint.{u1} (Set.{u1} R) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.completeBooleanAlgebra.{u1} R)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} R) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{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) (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) I)) -> (Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) (Ideal.map.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_3) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] [_inst_3 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2)] [_inst_4 : IsLocalization.{u2, u1} R _inst_1 M S _inst_2 _inst_3] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), (Ideal.IsPrime.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) I) -> (Disjoint.{u2} (Set.{u2} R) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} R) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} R) (Preorder.toLE.{u2} (Set.{u2} R) (PartialOrder.toPreorder.{u2} (Set.{u2} R) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} R) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} R) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} R) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} R) (Set.instCompleteBooleanAlgebraSet.{u2} R)))))) (SetLike.coe.{u2, u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) M) (SetLike.coe.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) I)) -> (Ideal.IsPrime.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2) (Ideal.map.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} S _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (algebraMap.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S _inst_2) _inst_3) I))
+Case conversion may be inaccurate. Consider using '#align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjointₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M`.
 This lemma gives the particular case for an ideal and its map,
@@ -151,6 +179,12 @@ theorem isPrime_of_isPrime_disjoint (I : Ideal R) (hp : I.IsPrime) (hd : Disjoin
   exact ⟨hp, hd⟩
 #align is_localization.is_prime_of_is_prime_disjoint IsLocalization.isPrime_of_isPrime_disjoint
 
+/- warning: is_localization.order_iso_of_prime -> IsLocalization.orderIsoOfPrime is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (S : Type.{u2}) [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_4 : IsLocalization.{u1, u2} R _inst_1 M S _inst_2 _inst_3], OrderIso.{u2, u1} (Subtype.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} R) (Preorder.toLE.{u1} (Set.{u1} R) (PartialOrder.toPreorder.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) M) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p)))) (Subtype.le.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Preorder.toLE.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (PartialOrder.toPreorder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (Submodule.completeLattice.{u2, u2} S S (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (fun (p : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) => Ideal.IsPrime.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2) p)) (Subtype.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (fun (p : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Disjoint.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} R) (Preorder.toLE.{u1} (Set.{u1} R) (PartialOrder.toPreorder.{u1} (Set.{u1} R) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} R) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} R) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} R) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} R) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} R) (Set.instCompleteBooleanAlgebraSet.{u1} R)))))) (SetLike.coe.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) M) (SetLike.coe.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) p))))
+Case conversion may be inaccurate. Consider using '#align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrimeₓ'. -/
 /-- If `R` is a ring, then prime ideals in the localization at `M`
 correspond to prime ideals in the original ring `R` that are disjoint from `M` -/
 def orderIsoOfPrime :
@@ -176,6 +210,12 @@ variable [Algebra R S] [IsLocalization M S]
 
 include M
 
+/- warning: is_localization.surjective_quotient_map_of_maximal_of_localization -> IsLocalization.surjective_quotientMap_of_maximal_of_localization is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toLE.{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)))))))) J (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)}, (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)) -> (Function.Surjective.{succ u1, succ 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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) 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_inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) => (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) -> (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I)) (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) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.hasQuotient.{u1} R _inst_1) J) (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) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (NonAssocRing.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) I) (Ring.toNonAssocRing.{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) I) (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) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] {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] {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {H : LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toLE.{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))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{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)))))))) J (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.instRingHomClassRingHom.{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.{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.instRingHomClassRingHom.{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)) -> (Function.Surjective.{succ u1, succ u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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_inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) => HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))) (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (RingHom.instRingHomClassRingHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R _inst_1) J) (Ideal.Quotient.commRing.{u1} R _inst_1 J)))) (Semiring.toNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToRing.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))))))) (Ideal.quotientMap.{u1, u2} R S _inst_1 _inst_2 J I (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) _inst_3) H)))
+Case conversion may be inaccurate. Consider using '#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localizationₓ'. -/
 /-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
   and the localization necessarily maps the equivalence class of the inverse in the localization -/
@@ -216,6 +256,12 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
 
 open nonZeroDivisors
 
+/- warning: is_localization.bot_lt_comap_prime -> IsLocalization.bot_lt_comap_prime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (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 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M S (CommRing.toCommSemiring.{u2} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toLE.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteSemilatticeInf.toPartialOrder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Submonoid.completeLattice.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))) M (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall (p : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) [hpp : Ideal.IsPrime.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) p], (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) p (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)))))) -> (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))) (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)))))))) (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))))) (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) p)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (M : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (S : Type.{u1}) [_inst_2 : CommRing.{u1} S] [_inst_3 : Algebra.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_4 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) M S (CommRing.toCommSemiring.{u1} S _inst_2) _inst_3] [_inst_5 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))) M (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) -> (forall (p : Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) [hpp : Ideal.IsPrime.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) p], (Ne.{succ u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) p (Bot.bot.{u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Submodule.instBotSubmodule.{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)))))) -> (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)))))))) (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))))) (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 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{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 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (algebraMap.{u2, u1} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) _inst_3) p)))
+Case conversion may be inaccurate. Consider using '#align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_primeₓ'. -/
 theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p.IsPrime]
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=
   by

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

@@ -220,8 +220,7 @@ theorem bot_lt_comap_prime [IsDomain R] (hM : M ≤ R⁰) (p : Ideal S) [hpp : p
     (hp0 : p ≠ ⊥) : ⊥ < Ideal.comap (algebraMap R S) p :=
   by
   haveI : IsDomain S := is_domain_of_le_non_zero_divisors _ hM
-  convert
-    (order_iso_of_prime M S).lt_iff_lt.mpr
+  convert(order_iso_of_prime M S).lt_iff_lt.mpr
       (show (⟨⊥, Ideal.bot_prime⟩ : { p : Ideal S // p.IsPrime }) < ⟨p, hpp⟩ from hp0.bot_lt)
   exact (Ideal.comap_bot_of_injective (algebraMap R S) (IsLocalization.injective _ hM)).symm
 #align is_localization.bot_lt_comap_prime IsLocalization.bot_lt_comap_prime

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.localization.ideal
-! leanprover-community/mathlib commit 926daa81fd8acb2a04e15572c4ff20af2753c2ae
+! leanprover-community/mathlib commit e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.RingTheory.Ideal.Operations
+import Mathbin.RingTheory.Ideal.QuotientOperations
 import Mathbin.RingTheory.Localization.Basic
 
 /-!

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -97,8 +97,8 @@ def orderEmbedding : Ideal S ↪o Ideal R where
   map_rel_iff' := by
     rintro J₁ J₂
     constructor
-    exact fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ
-    exact fun hJ => Ideal.comap_mono hJ
+    · exact fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ
+    · exact fun hJ => Ideal.comap_mono hJ
 #align is_localization.order_embedding IsLocalization.orderEmbedding
 
 /-- If `R` is a ring, then prime ideals in the localization at `M`
@@ -153,8 +153,8 @@ def orderIsoOfPrime :
   map_rel_iff' := by
     rintro I I'
     constructor
-    exact (fun h => show I.val ≤ I'.val from map_comap M S I.val ▸
-      map_comap M S I'.val ▸ Ideal.map_mono h)
+    · exact (fun h => show I.val ≤ I'.val from map_comap M S I.val ▸
+        map_comap M S I'.val ▸ Ideal.map_mono h)
     exact fun h x hx => h hx
 #align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrime
 

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

@@ -97,8 +97,8 @@ def orderEmbedding : Ideal S ↪o Ideal R where
   map_rel_iff' := by
     rintro J₁ J₂
     constructor
-    exact (fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ)
-    exact (fun hJ => Ideal.comap_mono hJ)
+    exact fun hJ => (map_comap M S) J₁ ▸ (map_comap M S) J₂ ▸ Ideal.map_mono hJ
+    exact fun hJ => Ideal.comap_mono hJ
 #align is_localization.order_embedding IsLocalization.orderEmbedding
 
 /-- If `R` is a ring, then prime ideals in the localization at `M`
@@ -155,7 +155,7 @@ def orderIsoOfPrime :
     constructor
     exact (fun h => show I.val ≤ I'.val from map_comap M S I.val ▸
       map_comap M S I'.val ▸ Ideal.map_mono h)
-    exact (fun h x hx => h hx)
+    exact fun h x hx => h hx
 #align is_localization.order_iso_of_prime IsLocalization.orderIsoOfPrime
 
 end CommSemiring

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)

@@ -23,7 +23,6 @@ namespace IsLocalization
 section CommSemiring
 
 variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemiring S]
-
 variable [Algebra R S] [IsLocalization M S]
 
 /-- Explicit characterization of the ideal given by `Ideal.map (algebraMap R S) I`.
@@ -164,7 +163,6 @@ end CommSemiring
 section CommRing
 
 variable {R : Type*} [CommRing R] (M : Submonoid R) (S : Type*) [CommRing S]
-
 variable [Algebra R S] [IsLocalization M S]
 
 /-- `quotientMap` applied to maximal ideals of a localization is `surjective`.

Classifies by adding issue number (#10691) to porting notes claiming was rw.

@@ -201,7 +201,7 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
               (Ideal.Quotient.eq_zero_iff_mem.2
                 (Ideal.mem_comap.2 (Ideal.Quotient.eq_zero_iff_mem.1 hn))))
           (_root_.trans hn ?_))
-    -- Porting note: was `rw`, but this took extremely long.
+    -- Porting note (#10691): was `rw`, but this took extremely long.
     refine Eq.trans ?_ (RingHom.map_mul (Ideal.Quotient.mk I) (algebraMap R S m) (mk' S 1 ⟨m, hm⟩))
     rw [← mk'_eq_mul_mk'_one, mk'_self, RingHom.map_one]
 #align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localization

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

This has nice performance benefits.

@@ -22,7 +22,7 @@ namespace IsLocalization
 
 section CommSemiring
 
-variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemiring S]
+variable {R : Type*} [CommSemiring R] (M : Submonoid R) (S : Type*) [CommSemiring S]
 
 variable [Algebra R S] [IsLocalization M S]
 
@@ -163,7 +163,7 @@ end CommSemiring
 
 section CommRing
 
-variable {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
+variable {R : Type*} [CommRing R] (M : Submonoid R) (S : Type*) [CommRing S]
 
 variable [Algebra R S] [IsLocalization M S]
 

• depends on: #5966

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

@@ -2,14 +2,12 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-! This file was ported from Lean 3 source module ring_theory.localization.ideal
-! leanprover-community/mathlib commit e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.RingTheory.Localization.Basic
 
+#align_import ring_theory.localization.ideal from "leanprover-community/mathlib"@"e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74"
+
 /-!
 # Ideals in localizations of commutative rings
 ## Implementation notes

Changes are of the form

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

@@ -70,7 +70,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} : z ∈ Ideal.map (algebraMap R
 theorem map_comap (J : Ideal S) : Ideal.map (algebraMap R S) (Ideal.comap (algebraMap R S) J) = J :=
   le_antisymm (Ideal.map_le_iff_le_comap.2 le_rfl) fun x hJ => by
     obtain ⟨r, s, hx⟩ := mk'_surjective M x
-    rw [← hx] at hJ⊢
+    rw [← hx] at hJ ⊢
     exact
       Ideal.mul_mem_right _ _
         (Ideal.mem_map_of_mem _

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

@@ -28,7 +28,7 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 
 variable [Algebra R S] [IsLocalization M S]
 
-/-- Explicit characterization of the ideal given by `Ideal.map (algebra_map R S) I`.
+/-- Explicit characterization of the ideal given by `Ideal.map (algebraMap R S) I`.
 In practice, this ideal differs only in that the carrier set is defined explicitly.
 This definition is only meant to be used in proving `mem_map_algebraMap_iff`,
 and any proof that needs to refer to the explicit carrier set should use that theorem. -/

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -57,7 +57,7 @@ theorem mem_map_algebraMap_iff {I : Ideal R} {z} : z ∈ Ideal.map (algebraMap R
     ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 := by
   constructor
   · change _ → z ∈ map_ideal M S I
-    refine' fun h => Ideal.mem_infₛ.1 h fun z hz => _
+    refine' fun h => Ideal.mem_sInf.1 h fun z hz => _
     obtain ⟨y, hy⟩ := hz
     let Z : { x // x ∈ I } := ⟨y, hy.left⟩
     use ⟨Z, 1⟩

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

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

@@ -53,9 +53,8 @@ private def map_ideal (I : Ideal R) : Ideal S where
     ring
 -- Porting note: removed #align declaration since it is a private def
 
-theorem mem_map_algebraMap_iff {I : Ideal R} {z} :
-    z ∈ Ideal.map (algebraMap R S) I ↔ ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 :=
-  by
+theorem mem_map_algebraMap_iff {I : Ideal R} {z} : z ∈ Ideal.map (algebraMap R S) I ↔
+    ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 := by
   constructor
   · change _ → z ∈ map_ideal M S I
     refine' fun h => Ideal.mem_infₛ.1 h fun z hz => _

@@ -13,7 +13,7 @@ import Mathlib.RingTheory.Localization.Basic
 /-!
 # Ideals in localizations of commutative rings
 ## Implementation notes
-See `src/ring_theory/localization/basic.lean` for a design overview.
+See `Mathlib/RingTheory/Localization/Basic.lean` for a design overview.
 ## Tags
 localization, ring localization, commutative ring localization, characteristic predicate,
 commutative ring, field of fractions
@@ -28,9 +28,9 @@ variable {R : Type _} [CommSemiring R] (M : Submonoid R) (S : Type _) [CommSemir
 
 variable [Algebra R S] [IsLocalization M S]
 
-/-- Explicit characterization of the ideal given by `ideal.map (algebra_map R S) I`.
+/-- Explicit characterization of the ideal given by `Ideal.map (algebra_map R S) I`.
 In practice, this ideal differs only in that the carrier set is defined explicitly.
-This definition is only meant to be used in proving `mem_map_algebra_map_iff`,
+This definition is only meant to be used in proving `mem_map_algebraMap_iff`,
 and any proof that needs to refer to the explicit carrier set should use that theorem. -/
 private def map_ideal (I : Ideal R) : Ideal S where
   carrier := { z : S | ∃ x : I × M, z * algebraMap R S x.2 = algebraMap R S x.1 }
@@ -170,7 +170,7 @@ variable {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
 
 variable [Algebra R S] [IsLocalization M S]
 
-/-- `quotient_map` applied to maximal ideals of a localization is `surjective`.
+/-- `quotientMap` applied to maximal ideals of a localization is `surjective`.
   The quotient by a maximal ideal is a field, so inverses to elements already exist,
   and the localization necessarily maps the equivalence class of the inverse in the localization -/
 theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPrime] {J : Ideal R}

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -207,8 +207,7 @@ theorem surjective_quotientMap_of_maximal_of_localization {I : Ideal S} [I.IsPri
     -- Porting note: was `rw`, but this took extremely long.
     refine Eq.trans ?_ (RingHom.map_mul (Ideal.Quotient.mk I) (algebraMap R S m) (mk' S 1 ⟨m, hm⟩))
     rw [← mk'_eq_mul_mk'_one, mk'_self, RingHom.map_one]
-#align is_localization.surjective_quotient_map_of_maximal_of_localization
-IsLocalization.surjective_quotientMap_of_maximal_of_localization
+#align is_localization.surjective_quotient_map_of_maximal_of_localization IsLocalization.surjective_quotientMap_of_maximal_of_localization
 
 open nonZeroDivisors
 

Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>