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

@@ -210,7 +210,7 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
           dsimp only
           induction n
           · rw [pow_zero, pow_zero]
-          · rw [pow_succ, pow_succ]
+          · rw [pow_succ', pow_succ']
             simpa only [mul] using congr_arg₂ (fun x y => mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) n_ih)
         a⟩
 
@@ -312,7 +312,7 @@ instance (r : R → R → Prop) : Semiring (RingQuot r)
   right_distrib := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [mul_quot, add_quot, right_distrib]
   npow n x := x ^ n
   npow_zero := by rintro ⟨⟨⟩⟩; simp [pow_quot, ← one_quot]
-  npow_succ := by rintro n ⟨⟨⟩⟩; simp [pow_quot, mul_quot, pow_succ]
+  npow_succ := by rintro n ⟨⟨⟩⟩; simp [pow_quot, mul_quot, pow_succ']
   nsmul := (· • ·)
   nsmul_zero := by rintro ⟨⟨⟩⟩; simp [smul_quot, ← zero_quot]
   nsmul_succ := by rintro n ⟨⟨⟩⟩; simp [smul_quot, add_quot, add_mul, add_comm]

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

@@ -473,8 +473,8 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
     (by
       refine' fun x h => Submodule.span_induction h _ _ _ _
       · rintro y ⟨a, b, h, su⟩
-        symm at su 
-        rw [← sub_eq_iff_eq_add] at su 
+        symm at su
+        rw [← sub_eq_iff_eq_add] at su
         rw [← su, RingHom.map_sub, mk_ring_hom_rel h, sub_self]
       · simp
       · intro a b ha hb; simp [ha, hb]

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Algebra.Algebra.Hom
-import Mathbin.RingTheory.Ideal.Quotient
+import Algebra.Algebra.Hom
+import RingTheory.Ideal.Quotient
 
 #align_import algebra.ring_quot from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -544,7 +544,7 @@ def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
     where
   unit := star' r hr
   star_involutive := by rintro ⟨⟨⟩⟩; simp [star'_quot]
-  star_mul := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, mul_quot, star_mul]
+  star_hMul := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, mul_quot, star_mul]
   star_add := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, add_quot, star_add]
 #align ring_quot.star_ring RingQuot.starRing
 -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.ring_quot
-! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Hom
 import Mathbin.RingTheory.Ideal.Quotient
 
+#align_import algebra.ring_quot from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 # Quotients of non-commutative rings
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -146,7 +146,7 @@ def ringCon (r : R → R → Prop) : RingCon R
 #print RingQuot.eqvGen_rel_eq /-
 theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r :=
   by
-  ext (x₁ x₂)
+  ext x₁ x₂
   constructor
   · intro h
     induction' h with x₃ x₄ h₃₄

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

@@ -47,11 +47,13 @@ instance (c : RingCon A) : Algebra S c.Quotient
   commutes' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.commutes _ _
   smul_def' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
 
+#print RingCon.coe_algebraMap /-
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
     (↑(algebraMap S A s) : c.Quotient) = algebraMap S _ s :=
   rfl
 #align ring_con.coe_algebra_map RingCon.coe_algebraMap
+-/
 
 end RingCon
 
@@ -70,21 +72,29 @@ inductive Rel (r : R → R → Prop) : R → R → Prop
 #align ring_quot.rel RingQuot.Rel
 -/
 
+#print RingQuot.Rel.add_right /-
 theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : Rel r (a + b) (a + c) := by
   rw [add_comm a b, add_comm a c]; exact rel.add_left h
 #align ring_quot.rel.add_right RingQuot.Rel.add_right
+-/
 
+#print RingQuot.Rel.neg /-
 theorem Rel.neg {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b : R⦄ (h : Rel r a b) :
     Rel r (-a) (-b) := by simp only [neg_eq_neg_one_mul a, neg_eq_neg_one_mul b, rel.mul_right h]
 #align ring_quot.rel.neg RingQuot.Rel.neg
+-/
 
+#print RingQuot.Rel.sub_left /-
 theorem Rel.sub_left {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r a b) :
     Rel r (a - c) (b - c) := by simp only [sub_eq_add_neg, h.add_left]
 #align ring_quot.rel.sub_left RingQuot.Rel.sub_left
+-/
 
+#print RingQuot.Rel.sub_right /-
 theorem Rel.sub_right {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) :
     Rel r (a - b) (a - c) := by simp only [sub_eq_add_neg, h.neg.add_right]
 #align ring_quot.rel.sub_right RingQuot.Rel.sub_right
+-/
 
 #print RingQuot.Rel.smul /-
 theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) : Rel r (k • a) (k • b) := by
@@ -92,6 +102,7 @@ theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) :
 #align ring_quot.rel.smul RingQuot.Rel.smul
 -/
 
+#print RingQuot.ringCon /-
 /-- `eqv_gen (ring_quot.rel r)` is a ring congruence. -/
 def ringCon (r : R → R → Prop) : RingCon R
     where
@@ -130,7 +141,9 @@ def ringCon (r : R → R → Prop) : RingCon R
     · exact (hab_ih _ _ <| hcd.symm _ _).symm _ _
     · exact (ihcd' _ _ hcd).trans _ _ _ (ihde' _ _ <| EqvGen.refl _)
 #align ring_quot.ring_con RingQuot.ringCon
+-/
 
+#print RingQuot.eqvGen_rel_eq /-
 theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r :=
   by
   ext (x₁ x₂)
@@ -154,6 +167,7 @@ theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r
     · exact (RingQuot.ringCon r).add ‹_› ‹_›
     · exact (RingQuot.ringCon r).mul ‹_› ‹_›
 #align ring_quot.eqv_gen_rel_eq RingQuot.eqvGen_rel_eq
+-/
 
 end RingQuot
 
@@ -230,38 +244,54 @@ instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Sub (RingQuot r) :=
 instance [Algebra S R] : SMul S (RingQuot r) :=
   ⟨smul r⟩
 
+#print RingQuot.zero_quot /-
 theorem zero_quot : (⟨Quot.mk _ 0⟩ : RingQuot r) = 0 :=
   show _ = zero r by rw [zero]
 #align ring_quot.zero_quot RingQuot.zero_quot
+-/
 
+#print RingQuot.one_quot /-
 theorem one_quot : (⟨Quot.mk _ 1⟩ : RingQuot r) = 1 :=
   show _ = one r by rw [one]
 #align ring_quot.one_quot RingQuot.one_quot
+-/
 
+#print RingQuot.add_quot /-
 theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a + b)⟩ := by
   show add r _ _ = _; rw [add]; rfl
 #align ring_quot.add_quot RingQuot.add_quot
+-/
 
+#print RingQuot.mul_quot /-
 theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a * b)⟩ := by
   show mul r _ _ = _; rw [mul]; rfl
 #align ring_quot.mul_quot RingQuot.mul_quot
+-/
 
+#print RingQuot.pow_quot /-
 theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.mk _ (a ^ n)⟩ := by
   show npow r _ _ = _; rw [npow]
 #align ring_quot.pow_quot RingQuot.pow_quot
+-/
 
+#print RingQuot.neg_quot /-
 theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
     (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ := by show neg r _ = _; rw [neg]; rfl
 #align ring_quot.neg_quot RingQuot.neg_quot
+-/
 
+#print RingQuot.sub_quot /-
 theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
     (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ := by show sub r _ _ = _;
   rw [sub]; rfl
 #align ring_quot.sub_quot RingQuot.sub_quot
+-/
 
+#print RingQuot.smul_quot /-
 theorem smul_quot [Algebra S R] {n : S} {a : R} :
     (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ := by show smul r _ _ = _; rw [smul]; rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
+-/
 
 instance (r : R → R → Prop) : Semiring (RingQuot r)
     where
@@ -321,6 +351,7 @@ instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r)
   commutes' r := by rintro ⟨⟨a⟩⟩; simp [Algebra.commutes, mul_quot]
   smul_def' r := by rintro ⟨⟨a⟩⟩; simp [smul_quot, Algebra.smul_def, mul_quot]
 
+#print RingQuot.mkRingHom /-
 /-- The quotient map from a ring to its quotient, as a homomorphism of rings.
 -/
 irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
@@ -330,15 +361,21 @@ irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
     map_zero' := by simp [← zero_quot]
     map_add' := by simp [add_quot] }
 #align ring_quot.mk_ring_hom RingQuot.mkRingHom
+-/
 
+#print RingQuot.mkRingHom_rel /-
 theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r x = mkRingHom r y := by
   simp [mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_rel
+-/
 
+#print RingQuot.mkRingHom_surjective /-
 theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) := by
   dsimp [mk_ring_hom]; rintro ⟨⟨⟩⟩; simp
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective
+-/
 
+#print RingQuot.ringQuot_ext /-
 @[ext]
 theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g : RingQuot r →+* T)
     (w : f.comp (mkRingHom r) = g.comp (mkRingHom r)) : f = g :=
@@ -347,9 +384,11 @@ theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g :
   rcases mk_ring_hom_surjective r x with ⟨x, rfl⟩
   exact (RingHom.congr_fun w x : _)
 #align ring_quot.ring_quot_ext RingQuot.ringQuot_ext
+-/
 
 variable {T : Type u₄} [Semiring T]
 
+#print RingQuot.lift /-
 /-- Any ring homomorphism `f : R →+* T` which respects a relation `r : R → R → Prop`
 factors uniquely through a morphism `ring_quot r →+* T`.
 -/
@@ -375,17 +414,23 @@ irreducible_def lift {r : R → R → Prop} :
     left_inv := fun f => by ext; simp [mk_ring_hom]
     right_inv := fun F => by ext; simp [mk_ring_hom] }
 #align ring_quot.lift RingQuot.lift
+-/
 
+#print RingQuot.lift_mkRingHom_apply /-
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
     lift ⟨f, w⟩ (mkRingHom r x) = f x := by simp_rw [lift, mk_ring_hom]; rfl
 #align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_apply
+-/
 
+#print RingQuot.lift_unique /-
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
     (g : RingQuot r →+* T) (h : g.comp (mkRingHom r) = f) : g = lift ⟨f, w⟩ := by ext; simp [h]
 #align ring_quot.lift_unique RingQuot.lift_unique
+-/
 
+#print RingQuot.eq_lift_comp_mkRingHom /-
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f = lift ⟨f.comp (mkRingHom r), fun x y h => by dsimp; rw [mk_ring_hom_rel h]⟩ :=
   by
@@ -393,6 +438,7 @@ theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
   rw [lift]
   rfl
 #align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHom
+-/
 
 section CommRing
 
@@ -404,13 +450,16 @@ agrees with the quotient by the appropriate ideal.
 
 variable {B : Type u₁} [CommRing B]
 
+#print RingQuot.ringQuotToIdealQuotient /-
 /-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift
     ⟨Ideal.Quotient.mk (Ideal.ofRel r), fun x y h =>
       Ideal.Quotient.eq.2 <| Submodule.mem_sInf.mpr fun p w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
+-/
 
+#print RingQuot.ringQuotToIdealQuotient_apply /-
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
     ringQuotToIdealQuotient r (mkRingHom r x) = Ideal.Quotient.mk _ x :=
@@ -418,7 +467,9 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
   simp_rw [ring_quot_to_ideal_quotient, lift, mk_ring_hom]
   rfl
 #align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_apply
+-/
 
+#print RingQuot.idealQuotientToRingQuot /-
 /-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
   Ideal.Quotient.lift (Ideal.ofRel r) (mkRingHom r)
@@ -432,13 +483,17 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
       · intro a b ha hb; simp [ha, hb]
       · intro a x hx; simp [hx])
 #align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuot
+-/
 
+#print RingQuot.idealQuotientToRingQuot_apply /-
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
     idealQuotientToRingQuot r (Ideal.Quotient.mk _ x) = mkRingHom r x :=
   rfl
 #align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_apply
+-/
 
+#print RingQuot.ringQuotEquivIdealQuotient /-
 /-- The ring equivalence between `ring_quot r` and `(ideal.of_rel r).quotient`
 -/
 def ringQuotEquivIdealQuotient (r : B → B → Prop) : RingQuot r ≃+* B ⧸ Ideal.ofRel r :=
@@ -456,6 +511,7 @@ def ringQuotEquivIdealQuotient (r : B → B → Prop) : RingQuot r ≃+* B ⧸ I
       rw [mk_ring_hom]
       rfl)
 #align ring_quot.ring_quot_equiv_ideal_quotient RingQuot.ringQuotEquivIdealQuotient
+-/
 
 end CommRing
 
@@ -463,8 +519,6 @@ section StarRing
 
 variable [StarRing R] (r) (hr : ∀ a b, r a b → r (star a) (star b))
 
-include hr
-
 #print RingQuot.Rel.star /-
 theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
   by
@@ -479,11 +533,14 @@ theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
 private irreducible_def star' : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (star : R → R) (Rel.star r hr) a⟩
 
+#print RingQuot.star'_quot /-
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
     (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := by show star' r _ _ = _;
   rw [star']; rfl
 #align ring_quot.star'_quot RingQuot.star'_quot
+-/
 
+#print RingQuot.starRing /-
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/
 def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
     (hr : ∀ a b, r a b → r (star a) (star b)) : StarRing (RingQuot r)
@@ -493,6 +550,7 @@ def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
   star_mul := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, mul_quot, star_mul]
   star_add := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, add_quot, star_add]
 #align ring_quot.star_ring RingQuot.starRing
+-/
 
 end StarRing
 
@@ -500,27 +558,36 @@ section Algebra
 
 variable (S)
 
+#print RingQuot.mkAlgHom /-
 /-- The quotient map from an `S`-algebra to its quotient, as a homomorphism of `S`-algebras.
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
   { mkRingHom s with commutes' := fun r => by simp [mk_ring_hom]; rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
+-/
 
+#print RingQuot.mkAlgHom_coe /-
 @[simp]
 theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s := by
   simp_rw [mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coe
+-/
 
+#print RingQuot.mkAlgHom_rel /-
 theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s x = mkAlgHom S s y :=
   by simp [mk_alg_hom, mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
+-/
 
+#print RingQuot.mkAlgHom_surjective /-
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
   dsimp [mk_alg_hom, mk_ring_hom]; rintro ⟨⟨a⟩⟩; use a; rfl
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective
+-/
 
 variable {B : Type u₄} [Semiring B] [Algebra S B]
 
+#print RingQuot.ringQuot_ext' /-
 @[ext]
 theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
     (w : f.comp (mkAlgHom S s) = g.comp (mkAlgHom S s)) : f = g :=
@@ -529,7 +596,9 @@ theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
   rcases mk_alg_hom_surjective S s x with ⟨x, rfl⟩
   exact (AlgHom.congr_fun w x : _)
 #align ring_quot.ring_quot_ext' RingQuot.ringQuot_ext'
+-/
 
+#print RingQuot.liftAlgHom /-
 /-- Any `S`-algebra homomorphism `f : A →ₐ[S] B` which respects a relation `s : A → A → Prop`
 factors uniquely through a morphism `ring_quot s →ₐ[S]  B`.
 -/
@@ -556,19 +625,25 @@ irreducible_def liftAlgHom {s : A → A → Prop} :
     left_inv := fun f => by ext; simp [mk_alg_hom, mk_ring_hom]
     right_inv := fun F => by ext; simp [mk_alg_hom, mk_ring_hom] }
 #align ring_quot.lift_alg_hom RingQuot.liftAlgHom
+-/
 
+#print RingQuot.liftAlgHom_mkAlgHom_apply /-
 @[simp]
 theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
     (w : ∀ ⦃x y⦄, s x y → f x = f y) (x) : (liftAlgHom S ⟨f, w⟩) ((mkAlgHom S s) x) = f x := by
   simp_rw [lift_alg_hom, mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.lift_alg_hom_mk_alg_hom_apply RingQuot.liftAlgHom_mkAlgHom_apply
+-/
 
+#print RingQuot.liftAlgHom_unique /-
 -- note this is essentially `(lift_alg_hom S).symm_apply_eq.mp h`
 theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ ⦃x y⦄, s x y → f x = f y)
     (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ := by ext;
   simp [h]
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
+-/
 
+#print RingQuot.eq_liftAlgHom_comp_mkAlgHom /-
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f = liftAlgHom S ⟨f.comp (mkAlgHom S s), fun x y h => by dsimp; erw [mk_alg_hom_rel S h]⟩ :=
   by
@@ -576,6 +651,7 @@ theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →
   rw [lift_alg_hom]
   rfl
 #align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHom
+-/
 
 end Algebra
 

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

@@ -187,7 +187,7 @@ private irreducible_def neg {R : Type u₁} [Ring R] (r : R → R → Prop) : Ri
   | ⟨a⟩ => ⟨Quot.map (fun a => -a) Rel.neg a⟩
 
 private irreducible_def sub {R : Type u₁} [Ring R] (r : R → R → Prop) :
-  RingQuot r → RingQuot r → RingQuot r
+    RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ Sub.sub Rel.sub_right Rel.sub_left a b⟩
 
 private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
@@ -354,7 +354,7 @@ variable {T : Type u₄} [Semiring T]
 factors uniquely through a morphism `ring_quot r →+* T`.
 -/
 irreducible_def lift {r : R → R → Prop} :
-  { f : R →+* T // ∀ ⦃x y⦄, r x y → f x = f y } ≃ (RingQuot r →+* T) :=
+    { f : R →+* T // ∀ ⦃x y⦄, r x y → f x = f y } ≃ (RingQuot r →+* T) :=
   { toFun := fun f' =>
       let f := (f' : R →+* T)
       { toFun := fun x =>
@@ -534,7 +534,7 @@ theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
 factors uniquely through a morphism `ring_quot s →ₐ[S]  B`.
 -/
 irreducible_def liftAlgHom {s : A → A → Prop} :
-  { f : A →ₐ[S] B // ∀ ⦃x y⦄, s x y → f x = f y } ≃ (RingQuot s →ₐ[S] B) :=
+    { f : A →ₐ[S] B // ∀ ⦃x y⦄, s x y → f x = f y } ≃ (RingQuot s →ₐ[S] B) :=
   { toFun := fun f' =>
       let f := (f' : A →ₐ[S] B)
       { toFun := fun x =>

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

@@ -425,8 +425,8 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
     (by
       refine' fun x h => Submodule.span_induction h _ _ _ _
       · rintro y ⟨a, b, h, su⟩
-        symm at su
-        rw [← sub_eq_iff_eq_add] at su
+        symm at su 
+        rw [← sub_eq_iff_eq_add] at su 
         rw [← su, RingHom.map_sub, mk_ring_hom_rel h, sub_self]
       · simp
       · intro a b ha hb; simp [ha, hb]

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

@@ -511,17 +511,13 @@ theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s
   simp_rw [mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coe
 
-#print RingQuot.mkAlgHom_rel /-
 theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s x = mkAlgHom S s y :=
   by simp [mk_alg_hom, mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
--/
 
-#print RingQuot.mkAlgHom_surjective /-
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
   dsimp [mk_alg_hom, mk_ring_hom]; rintro ⟨⟨a⟩⟩; use a; rfl
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective
--/
 
 variable {B : Type u₄} [Semiring B] [Algebra S B]
 
@@ -534,7 +530,6 @@ theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
   exact (AlgHom.congr_fun w x : _)
 #align ring_quot.ring_quot_ext' RingQuot.ringQuot_ext'
 
-#print RingQuot.liftAlgHom /-
 /-- Any `S`-algebra homomorphism `f : A →ₐ[S] B` which respects a relation `s : A → A → Prop`
 factors uniquely through a morphism `ring_quot s →ₐ[S]  B`.
 -/
@@ -561,23 +556,18 @@ irreducible_def liftAlgHom {s : A → A → Prop} :
     left_inv := fun f => by ext; simp [mk_alg_hom, mk_ring_hom]
     right_inv := fun F => by ext; simp [mk_alg_hom, mk_ring_hom] }
 #align ring_quot.lift_alg_hom RingQuot.liftAlgHom
--/
 
-#print RingQuot.liftAlgHom_mkAlgHom_apply /-
 @[simp]
 theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
     (w : ∀ ⦃x y⦄, s x y → f x = f y) (x) : (liftAlgHom S ⟨f, w⟩) ((mkAlgHom S s) x) = f x := by
   simp_rw [lift_alg_hom, mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.lift_alg_hom_mk_alg_hom_apply RingQuot.liftAlgHom_mkAlgHom_apply
--/
 
-#print RingQuot.liftAlgHom_unique /-
 -- note this is essentially `(lift_alg_hom S).symm_apply_eq.mp h`
 theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ ⦃x y⦄, s x y → f x = f y)
     (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ := by ext;
   simp [h]
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
--/
 
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f = liftAlgHom S ⟨f.comp (mkAlgHom S s), fun x y h => by dsimp; erw [mk_alg_hom_rel S h]⟩ :=

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

@@ -47,9 +47,6 @@ instance (c : RingCon A) : Algebra S c.Quotient
   commutes' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.commutes _ _
   smul_def' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
 
-/- warning: ring_con.coe_algebra_map -> RingCon.coe_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_con.coe_algebra_map RingCon.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
     (↑(algebraMap S A s) : c.Quotient) = algebraMap S _ s :=
@@ -73,42 +70,18 @@ inductive Rel (r : R → R → Prop) : R → R → Prop
 #align ring_quot.rel RingQuot.Rel
 -/
 
-/- warning: ring_quot.rel.add_right -> RingQuot.Rel.add_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R _inst_1 r b c) -> (RingQuot.Rel.{u1} R _inst_1 r (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a c))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R _inst_1 r b c) -> (RingQuot.Rel.{u1} R _inst_1 r (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a c))
-Case conversion may be inaccurate. Consider using '#align ring_quot.rel.add_right RingQuot.Rel.add_rightₓ'. -/
 theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : Rel r (a + b) (a + c) := by
   rw [add_comm a b, add_comm a c]; exact rel.add_left h
 #align ring_quot.rel.add_right RingQuot.Rel.add_right
 
-/- warning: ring_quot.rel.neg -> RingQuot.Rel.neg is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) a) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) b))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) a) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) b))
-Case conversion may be inaccurate. Consider using '#align ring_quot.rel.neg RingQuot.Rel.negₓ'. -/
 theorem Rel.neg {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b : R⦄ (h : Rel r a b) :
     Rel r (-a) (-b) := by simp only [neg_eq_neg_one_mul a, neg_eq_neg_one_mul b, rel.mul_right h]
 #align ring_quot.rel.neg RingQuot.Rel.neg
 
-/- warning: ring_quot.rel.sub_left -> RingQuot.Rel.sub_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a c) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) b c))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a c) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) b c))
-Case conversion may be inaccurate. Consider using '#align ring_quot.rel.sub_left RingQuot.Rel.sub_leftₓ'. -/
 theorem Rel.sub_left {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r a b) :
     Rel r (a - c) (b - c) := by simp only [sub_eq_add_neg, h.add_left]
 #align ring_quot.rel.sub_left RingQuot.Rel.sub_left
 
-/- warning: ring_quot.rel.sub_right -> RingQuot.Rel.sub_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r b c) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a b) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a c))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r b c) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a b) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a c))
-Case conversion may be inaccurate. Consider using '#align ring_quot.rel.sub_right RingQuot.Rel.sub_rightₓ'. -/
 theorem Rel.sub_right {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) :
     Rel r (a - b) (a - c) := by simp only [sub_eq_add_neg, h.neg.add_right]
 #align ring_quot.rel.sub_right RingQuot.Rel.sub_right
@@ -119,12 +92,6 @@ theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) :
 #align ring_quot.rel.smul RingQuot.Rel.smul
 -/
 
-/- warning: ring_quot.ring_con -> RingQuot.ringCon is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (R -> R -> Prop) -> (RingCon.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (R -> R -> Prop) -> (RingCon.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_con RingQuot.ringConₓ'. -/
 /-- `eqv_gen (ring_quot.rel r)` is a ring congruence. -/
 def ringCon (r : R → R → Prop) : RingCon R
     where
@@ -164,12 +131,6 @@ def ringCon (r : R → R → Prop) : RingCon R
     · exact (ihcd' _ _ hcd).trans _ _ _ (ihde' _ _ <| EqvGen.refl _)
 #align ring_quot.ring_con RingQuot.ringCon
 
-/- warning: ring_quot.eqv_gen_rel_eq -> RingQuot.eqvGen_rel_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (R -> R -> Prop) (EqvGen.{u1} R (RingQuot.Rel.{u1} R _inst_1 r)) (RingConGen.Rel.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) r)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (R -> R -> Prop) (EqvGen.{u1} R (RingQuot.Rel.{u1} R _inst_1 r)) (RingConGen.Rel.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) r)
-Case conversion may be inaccurate. Consider using '#align ring_quot.eqv_gen_rel_eq RingQuot.eqvGen_rel_eqₓ'. -/
 theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r :=
   by
   ext (x₁ x₂)
@@ -269,83 +230,35 @@ instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Sub (RingQuot r) :=
 instance [Algebra S R] : SMul S (RingQuot r) :=
   ⟨smul r⟩
 
-/- warning: ring_quot.zero_quot -> RingQuot.zero_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 0 (OfNat.mk.{u1} (RingQuot.{u1} R _inst_1 r) 0 (Zero.zero.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasZero.{u1} R _inst_1 r))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 0 (Zero.toOfNat0.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instZeroRingQuot.{u1} R _inst_1 r)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.zero_quot RingQuot.zero_quotₓ'. -/
 theorem zero_quot : (⟨Quot.mk _ 0⟩ : RingQuot r) = 0 :=
   show _ = zero r by rw [zero]
 #align ring_quot.zero_quot RingQuot.zero_quot
 
-/- warning: ring_quot.one_quot -> RingQuot.one_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 1 (OfNat.mk.{u1} (RingQuot.{u1} R _inst_1 r) 1 (One.one.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasOne.{u1} R _inst_1 r))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 1 (One.toOfNat1.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instOneRingQuot.{u1} R _inst_1 r)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.one_quot RingQuot.one_quotₓ'. -/
 theorem one_quot : (⟨Quot.mk _ 1⟩ : RingQuot r) = 1 :=
   show _ = one r by rw [one]
 #align ring_quot.one_quot RingQuot.one_quot
 
-/- warning: ring_quot.add_quot -> RingQuot.add_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHAdd.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasAdd.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHAdd.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instAddRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.add_quot RingQuot.add_quotₓ'. -/
 theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a + b)⟩ := by
   show add r _ _ = _; rw [add]; rfl
 #align ring_quot.add_quot RingQuot.add_quot
 
-/- warning: ring_quot.mul_quot -> RingQuot.mul_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHMul.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasMul.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHMul.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instMulRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a b)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.mul_quot RingQuot.mul_quotₓ'. -/
 theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a * b)⟩ := by
   show mul r _ _ = _; rw [mul]; rfl
 #align ring_quot.mul_quot RingQuot.mul_quot
 
-/- warning: ring_quot.pow_quot -> RingQuot.pow_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {n : Nat}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.{u1} R _inst_1 r) (instHPow.{u1, 0} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.Nat.hasPow.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) n) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) a n)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {n : Nat}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.{u1} R _inst_1 r) (instHPow.{u1, 0} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.instPowRingQuotNat.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) n) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) a n)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.pow_quot RingQuot.pow_quotₓ'. -/
 theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.mk _ (a ^ n)⟩ := by
   show npow r _ _ = _; rw [npow]
 #align ring_quot.pow_quot RingQuot.pow_quot
 
-/- warning: ring_quot.neg_quot -> RingQuot.neg_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.hasNeg.{u1} R _inst_5 r) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) a)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instNegRingQuotToSemiring.{u1} R _inst_5 r) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) a)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.neg_quot RingQuot.neg_quotₓ'. -/
 theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
     (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ := by show neg r _ = _; rw [neg]; rfl
 #align ring_quot.neg_quot RingQuot.neg_quot
 
-/- warning: ring_quot.sub_quot -> RingQuot.sub_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (instHSub.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.hasSub.{u1} R _inst_5 r)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) b))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a b)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (instHSub.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instSubRingQuotToSemiring.{u1} R _inst_5 r)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) b))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a b)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.sub_quot RingQuot.sub_quotₓ'. -/
 theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
     (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ := by show sub r _ _ = _;
   rw [sub]; rfl
 #align ring_quot.sub_quot RingQuot.sub_quot
 
-/- warning: ring_quot.smul_quot -> RingQuot.smul_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (r : R -> R -> Prop) [_inst_5 : Algebra.{u2, u1} S R _inst_2 _inst_1] {n : S} {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (SMul.smul.{u2, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.hasSmul.{u1, u2} R _inst_1 S _inst_2 r _inst_5) n (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (SMul.smul.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSmulZeroClass.{u2, u1} S R (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} S R (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u2, u1} S R (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Algebra.toModule.{u2, u1} S R _inst_2 _inst_1 _inst_5))))) n a)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (r : R -> R -> Prop) [_inst_5 : Algebra.{u2, u1} S R _inst_2 _inst_1] {n : S} {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHSMul.{u2, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.instSMulRingQuot.{u1, u2} R _inst_1 S _inst_2 r _inst_5)) n (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R (Algebra.toSMul.{u2, u1} S R _inst_2 _inst_1 _inst_5)) n a)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.smul_quot RingQuot.smul_quotₓ'. -/
 theorem smul_quot [Algebra S R] {n : S} {a : R} :
     (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ := by show smul r _ _ = _; rw [smul]; rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
@@ -408,12 +321,6 @@ instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r)
   commutes' r := by rintro ⟨⟨a⟩⟩; simp [Algebra.commutes, mul_quot]
   smul_def' r := by rintro ⟨⟨a⟩⟩; simp [smul_quot, Algebra.smul_def, mul_quot]
 
-/- warning: ring_quot.mk_ring_hom -> RingQuot.mkRingHom is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))
-Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom RingQuot.mkRingHomₓ'. -/
 /-- The quotient map from a ring to its quotient, as a homomorphism of rings.
 -/
 irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
@@ -424,32 +331,14 @@ irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
     map_add' := by simp [add_quot] }
 #align ring_quot.mk_ring_hom RingQuot.mkRingHom
 
-/- warning: ring_quot.mk_ring_hom_rel -> RingQuot.mkRingHom_rel is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
-Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_relₓ'. -/
 theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r x = mkRingHom r y := by
   simp [mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_rel
 
-/- warning: ring_quot.mk_ring_hom_surjective -> RingQuot.mkRingHom_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
-Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjectiveₓ'. -/
 theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) := by
   dsimp [mk_ring_hom]; rintro ⟨⟨⟩⟩; simp
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective
 
-/- warning: ring_quot.ring_quot_ext -> RingQuot.ringQuot_ext is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r))) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f g)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r))) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f g)
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_ext RingQuot.ringQuot_extₓ'. -/
 @[ext]
 theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g : RingQuot r →+* T)
     (w : f.comp (mkRingHom r) = g.comp (mkRingHom r)) : f = g :=
@@ -461,12 +350,6 @@ theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g :
 
 variable {T : Type u₄} [Semiring T]
 
-/- warning: ring_quot.lift -> RingQuot.lift is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
-Case conversion may be inaccurate. Consider using '#align ring_quot.lift RingQuot.liftₓ'. -/
 /-- Any ring homomorphism `f : R →+* T` which respects a relation `r : R → R → Prop`
 factors uniquely through a morphism `ring_quot r →+* T`.
 -/
@@ -493,25 +376,16 @@ irreducible_def lift {r : R → R → Prop} :
     right_inv := fun F => by ext; simp [mk_ring_hom] }
 #align ring_quot.lift RingQuot.lift
 
-/- warning: ring_quot.lift_mk_ring_hom_apply -> RingQuot.lift_mkRingHom_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_applyₓ'. -/
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
     lift ⟨f, w⟩ (mkRingHom r x) = f x := by simp_rw [lift, mk_ring_hom]; rfl
 #align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_apply
 
-/- warning: ring_quot.lift_unique -> RingQuot.lift_unique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.lift_unique RingQuot.lift_uniqueₓ'. -/
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
     (g : RingQuot r →+* T) (h : g.comp (mkRingHom r) = f) : g = lift ⟨f, w⟩ := by ext; simp [h]
 #align ring_quot.lift_unique RingQuot.lift_unique
 
-/- warning: ring_quot.eq_lift_comp_mk_ring_hom -> RingQuot.eq_lift_comp_mkRingHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f = lift ⟨f.comp (mkRingHom r), fun x y h => by dsimp; rw [mk_ring_hom_rel h]⟩ :=
   by
@@ -530,12 +404,6 @@ agrees with the quotient by the appropriate ideal.
 
 variable {B : Type u₁} [CommRing B]
 
-/- warning: ring_quot.ring_quot_to_ideal_quotient -> RingQuot.ringQuotToIdealQuotient is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
-but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotientₓ'. -/
 /-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift
@@ -543,9 +411,6 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
       Ideal.Quotient.eq.2 <| Submodule.mem_sInf.mpr fun p w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 
-/- warning: ring_quot.ring_quot_to_ideal_quotient_apply -> RingQuot.ringQuotToIdealQuotient_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
     ringQuotToIdealQuotient r (mkRingHom r x) = Ideal.Quotient.mk _ x :=
@@ -554,12 +419,6 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
   rfl
 #align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_apply
 
-/- warning: ring_quot.ideal_quotient_to_ring_quot -> RingQuot.idealQuotientToRingQuot is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))
-but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))
-Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuotₓ'. -/
 /-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
   Ideal.Quotient.lift (Ideal.ofRel r) (mkRingHom r)
@@ -574,21 +433,12 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
       · intro a x hx; simp [hx])
 #align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuot
 
-/- warning: ring_quot.ideal_quotient_to_ring_quot_apply -> RingQuot.idealQuotientToRingQuot_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
     idealQuotientToRingQuot r (Ideal.Quotient.mk _ x) = mkRingHom r x :=
   rfl
 #align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_apply
 
-/- warning: ring_quot.ring_quot_equiv_ideal_quotient -> RingQuot.ringQuotEquivIdealQuotient is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Distrib.toHasMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasAdd.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))))) (Distrib.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))
-but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.instMulRingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocRing.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.instAddRingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Distrib.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_equiv_ideal_quotient RingQuot.ringQuotEquivIdealQuotientₓ'. -/
 /-- The ring equivalence between `ring_quot r` and `(ideal.of_rel r).quotient`
 -/
 def ringQuotEquivIdealQuotient (r : B → B → Prop) : RingQuot r ≃+* B ⧸ Ideal.ofRel r :=
@@ -629,23 +479,11 @@ theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
 private irreducible_def star' : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (star : R → R) (Rel.star r hr) a⟩
 
-/- warning: ring_quot.star'_quot -> RingQuot.star'_quot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.2156597245.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_private.Mathlib.Algebra.RingQuot.0.RingQuot.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.star'_quot RingQuot.star'_quotₓ'. -/
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
     (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := by show star' r _ _ = _;
   rw [star']; rfl
 #align ring_quot.star'_quot RingQuot.star'_quot
 
-/- warning: ring_quot.star_ring -> RingQuot.starRing is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_7 : Semiring.{u1} R] [_inst_8 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)] (r : R -> R -> Prop), (forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) b))) -> (StarRing.{u1} (RingQuot.{u1} R _inst_7 r) (Semiring.toNonUnitalSemiring.{u1} (RingQuot.{u1} R _inst_7 r) (RingQuot.semiring.{u1} R _inst_7 r)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_7 : Semiring.{u1} R] [_inst_8 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)] (r : R -> R -> Prop), (forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) b))) -> (StarRing.{u1} (RingQuot.{u1} R _inst_7 r) (Semiring.toNonUnitalSemiring.{u1} (RingQuot.{u1} R _inst_7 r) (RingQuot.instSemiring.{u1} R _inst_7 r)))
-Case conversion may be inaccurate. Consider using '#align ring_quot.star_ring RingQuot.starRingₓ'. -/
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/
 def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
     (hr : ∀ a b, r a b → r (star a) (star b)) : StarRing (RingQuot r)
@@ -662,21 +500,12 @@ section Algebra
 
 variable (S)
 
-/- warning: ring_quot.mk_alg_hom -> RingQuot.mkAlgHom is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)
-Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom RingQuot.mkAlgHomₓ'. -/
 /-- The quotient map from an `S`-algebra to its quotient, as a homomorphism of `S`-algebras.
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
   { mkRingHom s with commutes' := fun r => by simp [mk_ring_hom]; rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
-/- warning: ring_quot.mk_alg_hom_coe -> RingQuot.mkAlgHom_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coeₓ'. -/
 @[simp]
 theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s := by
   simp_rw [mk_alg_hom, mk_ring_hom]; rfl
@@ -696,12 +525,6 @@ theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgH
 
 variable {B : Type u₄} [Semiring B] [Algebra S B]
 
-/- warning: ring_quot.ring_quot_ext' -> RingQuot.ringQuot_ext' is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (g : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 g (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s))) -> (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f g)
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (g : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 g (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s))) -> (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f g)
-Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_ext' RingQuot.ringQuot_ext'ₓ'. -/
 @[ext]
 theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
     (w : f.comp (mkAlgHom S s) = g.comp (mkAlgHom S s)) : f = g :=
@@ -756,9 +579,6 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
 -/
 
-/- warning: ring_quot.eq_lift_alg_hom_comp_mk_alg_hom -> RingQuot.eq_liftAlgHom_comp_mkAlgHom is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f = liftAlgHom S ⟨f.comp (mkAlgHom S s), fun x y h => by dsimp; erw [mk_alg_hom_rel S h]⟩ :=
   by

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

@@ -79,10 +79,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R _inst_1 r b c) -> (RingQuot.Rel.{u1} R _inst_1 r (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a c))
 Case conversion may be inaccurate. Consider using '#align ring_quot.rel.add_right RingQuot.Rel.add_rightₓ'. -/
-theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : Rel r (a + b) (a + c) :=
-  by
-  rw [add_comm a b, add_comm a c]
-  exact rel.add_left h
+theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : Rel r (a + b) (a + c) := by
+  rw [add_comm a b, add_comm a c]; exact rel.add_left h
 #align ring_quot.rel.add_right RingQuot.Rel.add_right
 
 /- warning: ring_quot.rel.neg -> RingQuot.Rel.neg is a dubious translation:
@@ -297,11 +295,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHAdd.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instAddRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.add_quot RingQuot.add_quotₓ'. -/
-theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a + b)⟩ :=
-  by
-  show add r _ _ = _
-  rw [add]
-  rfl
+theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a + b)⟩ := by
+  show add r _ _ = _; rw [add]; rfl
 #align ring_quot.add_quot RingQuot.add_quot
 
 /- warning: ring_quot.mul_quot -> RingQuot.mul_quot is a dubious translation:
@@ -310,11 +305,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHMul.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instMulRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a b)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.mul_quot RingQuot.mul_quotₓ'. -/
-theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a * b)⟩ :=
-  by
-  show mul r _ _ = _
-  rw [mul]
-  rfl
+theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a * b)⟩ := by
+  show mul r _ _ = _; rw [mul]; rfl
 #align ring_quot.mul_quot RingQuot.mul_quot
 
 /- warning: ring_quot.pow_quot -> RingQuot.pow_quot is a dubious translation:
@@ -323,10 +315,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {n : Nat}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.{u1} R _inst_1 r) (instHPow.{u1, 0} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.instPowRingQuotNat.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) n) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) a n)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.pow_quot RingQuot.pow_quotₓ'. -/
-theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.mk _ (a ^ n)⟩ :=
-  by
-  show npow r _ _ = _
-  rw [npow]
+theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.mk _ (a ^ n)⟩ := by
+  show npow r _ _ = _; rw [npow]
 #align ring_quot.pow_quot RingQuot.pow_quot
 
 /- warning: ring_quot.neg_quot -> RingQuot.neg_quot is a dubious translation:
@@ -336,11 +326,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instNegRingQuotToSemiring.{u1} R _inst_5 r) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) a)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.neg_quot RingQuot.neg_quotₓ'. -/
 theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
-    (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ :=
-  by
-  show neg r _ = _
-  rw [neg]
-  rfl
+    (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ := by show neg r _ = _; rw [neg]; rfl
 #align ring_quot.neg_quot RingQuot.neg_quot
 
 /- warning: ring_quot.sub_quot -> RingQuot.sub_quot is a dubious translation:
@@ -350,11 +336,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (instHSub.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instSubRingQuotToSemiring.{u1} R _inst_5 r)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) b))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a b)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.sub_quot RingQuot.sub_quotₓ'. -/
 theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
-    (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ :=
-  by
-  show sub r _ _ = _
-  rw [sub]
-  rfl
+    (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ := by show sub r _ _ = _;
+  rw [sub]; rfl
 #align ring_quot.sub_quot RingQuot.sub_quot
 
 /- warning: ring_quot.smul_quot -> RingQuot.smul_quot is a dubious translation:
@@ -364,11 +347,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (r : R -> R -> Prop) [_inst_5 : Algebra.{u2, u1} S R _inst_2 _inst_1] {n : S} {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHSMul.{u2, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.instSMulRingQuot.{u1, u2} R _inst_1 S _inst_2 r _inst_5)) n (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R (Algebra.toSMul.{u2, u1} S R _inst_2 _inst_1 _inst_5)) n a)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.smul_quot RingQuot.smul_quotₓ'. -/
 theorem smul_quot [Algebra S R] {n : S} {a : R} :
-    (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ :=
-  by
-  show smul r _ _ = _
-  rw [smul]
-  rfl
+    (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ := by show smul r _ _ = _; rw [smul]; rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
 
 instance (r : R → R → Prop) : Semiring (RingQuot r)
@@ -380,80 +359,37 @@ instance (r : R → R → Prop) : Semiring (RingQuot r)
   natCast := natCast r
   natCast_zero := by simp [Nat.cast, nat_cast, ← zero_quot]
   natCast_succ := by simp [Nat.cast, nat_cast, ← one_quot, add_quot]
-  add_assoc := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [add_quot, add_assoc]
-  zero_add := by
-    rintro ⟨⟨⟩⟩
-    simp [add_quot, ← zero_quot]
-  add_zero := by
-    rintro ⟨⟨⟩⟩
-    simp [add_quot, ← zero_quot]
-  zero_mul := by
-    rintro ⟨⟨⟩⟩
-    simp [mul_quot, ← zero_quot]
-  mul_zero := by
-    rintro ⟨⟨⟩⟩
-    simp [mul_quot, ← zero_quot]
-  add_comm := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [add_quot, add_comm]
-  mul_assoc := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [mul_quot, mul_assoc]
-  one_mul := by
-    rintro ⟨⟨⟩⟩
-    simp [mul_quot, ← one_quot]
-  mul_one := by
-    rintro ⟨⟨⟩⟩
-    simp [mul_quot, ← one_quot]
-  left_distrib := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [mul_quot, add_quot, left_distrib]
-  right_distrib := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [mul_quot, add_quot, right_distrib]
+  add_assoc := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [add_quot, add_assoc]
+  zero_add := by rintro ⟨⟨⟩⟩; simp [add_quot, ← zero_quot]
+  add_zero := by rintro ⟨⟨⟩⟩; simp [add_quot, ← zero_quot]
+  zero_mul := by rintro ⟨⟨⟩⟩; simp [mul_quot, ← zero_quot]
+  mul_zero := by rintro ⟨⟨⟩⟩; simp [mul_quot, ← zero_quot]
+  add_comm := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [add_quot, add_comm]
+  mul_assoc := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [mul_quot, mul_assoc]
+  one_mul := by rintro ⟨⟨⟩⟩; simp [mul_quot, ← one_quot]
+  mul_one := by rintro ⟨⟨⟩⟩; simp [mul_quot, ← one_quot]
+  left_distrib := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [mul_quot, add_quot, left_distrib]
+  right_distrib := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [mul_quot, add_quot, right_distrib]
   npow n x := x ^ n
-  npow_zero := by
-    rintro ⟨⟨⟩⟩
-    simp [pow_quot, ← one_quot]
-  npow_succ := by
-    rintro n ⟨⟨⟩⟩
-    simp [pow_quot, mul_quot, pow_succ]
+  npow_zero := by rintro ⟨⟨⟩⟩; simp [pow_quot, ← one_quot]
+  npow_succ := by rintro n ⟨⟨⟩⟩; simp [pow_quot, mul_quot, pow_succ]
   nsmul := (· • ·)
-  nsmul_zero := by
-    rintro ⟨⟨⟩⟩
-    simp [smul_quot, ← zero_quot]
-  nsmul_succ := by
-    rintro n ⟨⟨⟩⟩
-    simp [smul_quot, add_quot, add_mul, add_comm]
+  nsmul_zero := by rintro ⟨⟨⟩⟩; simp [smul_quot, ← zero_quot]
+  nsmul_succ := by rintro n ⟨⟨⟩⟩; simp [smul_quot, add_quot, add_mul, add_comm]
 
 instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
   { RingQuot.semiring r with
     neg := Neg.neg
-    add_left_neg := by
-      rintro ⟨⟨⟩⟩
-      simp [neg_quot, add_quot, ← zero_quot]
+    add_left_neg := by rintro ⟨⟨⟩⟩; simp [neg_quot, add_quot, ← zero_quot]
     sub := Sub.sub
-    sub_eq_add_neg := by
-      rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-      simp [neg_quot, sub_quot, add_quot, sub_eq_add_neg]
+    sub_eq_add_neg := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [neg_quot, sub_quot, add_quot, sub_eq_add_neg]
     zsmul := (· • ·)
-    zsmul_zero' := by
-      rintro ⟨⟨⟩⟩
-      simp [smul_quot, ← zero_quot]
-    zsmul_succ' := by
-      rintro n ⟨⟨⟩⟩
-      simp [smul_quot, add_quot, add_mul, add_comm]
-    zsmul_neg' := by
-      rintro n ⟨⟨⟩⟩
-      simp [smul_quot, neg_quot, add_mul] }
+    zsmul_zero' := by rintro ⟨⟨⟩⟩; simp [smul_quot, ← zero_quot]
+    zsmul_succ' := by rintro n ⟨⟨⟩⟩; simp [smul_quot, add_quot, add_mul, add_comm]
+    zsmul_neg' := by rintro n ⟨⟨⟩⟩; simp [smul_quot, neg_quot, add_mul] }
 
 instance {R : Type u₁} [CommSemiring R] (r : R → R → Prop) : CommSemiring (RingQuot r) :=
-  { RingQuot.semiring r with
-    mul_comm := by
-      rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-      simp [mul_quot, mul_comm] }
+  { RingQuot.semiring r with mul_comm := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [mul_quot, mul_comm] }
 
 instance {R : Type u₁} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
   { RingQuot.commSemiring r, RingQuot.ring r with }
@@ -469,12 +405,8 @@ instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r)
   map_mul' := by simp [mul_quot]
   map_zero' := by simp [← zero_quot]
   map_add' := by simp [add_quot]
-  commutes' r := by
-    rintro ⟨⟨a⟩⟩
-    simp [Algebra.commutes, mul_quot]
-  smul_def' r := by
-    rintro ⟨⟨a⟩⟩
-    simp [smul_quot, Algebra.smul_def, mul_quot]
+  commutes' r := by rintro ⟨⟨a⟩⟩; simp [Algebra.commutes, mul_quot]
+  smul_def' r := by rintro ⟨⟨a⟩⟩; simp [smul_quot, Algebra.smul_def, mul_quot]
 
 /- warning: ring_quot.mk_ring_hom -> RingQuot.mkRingHom is a dubious translation:
 lean 3 declaration is
@@ -508,11 +440,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
 Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjectiveₓ'. -/
-theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) :=
-  by
-  dsimp [mk_ring_hom]
-  rintro ⟨⟨⟩⟩
-  simp
+theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) := by
+  dsimp [mk_ring_hom]; rintro ⟨⟨⟩⟩; simp
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective
 
 /- warning: ring_quot.ring_quot_ext -> RingQuot.ringQuot_ext is a dubious translation:
@@ -556,23 +485,12 @@ irreducible_def lift {r : R → R → Prop} :
               case mul_right _ _ _ _ r' => simp [r'])
             x.toQuot
         map_zero' := by simp [← zero_quot, f.map_zero]
-        map_add' := by
-          rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩
-          simp [add_quot, f.map_add x y]
+        map_add' := by rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩; simp [add_quot, f.map_add x y]
         map_one' := by simp [← one_quot, f.map_one]
-        map_mul' := by
-          rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩
-          simp [mul_quot, f.map_mul x y] }
-    invFun := fun F =>
-      ⟨F.comp (mkRingHom r), fun x y h => by
-        dsimp
-        rw [mk_ring_hom_rel h]⟩
-    left_inv := fun f => by
-      ext
-      simp [mk_ring_hom]
-    right_inv := fun F => by
-      ext
-      simp [mk_ring_hom] }
+        map_mul' := by rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩; simp [mul_quot, f.map_mul x y] }
+    invFun := fun F => ⟨F.comp (mkRingHom r), fun x y h => by dsimp; rw [mk_ring_hom_rel h]⟩
+    left_inv := fun f => by ext; simp [mk_ring_hom]
+    right_inv := fun F => by ext; simp [mk_ring_hom] }
 #align ring_quot.lift RingQuot.lift
 
 /- warning: ring_quot.lift_mk_ring_hom_apply -> RingQuot.lift_mkRingHom_apply is a dubious translation:
@@ -580,10 +498,7 @@ irreducible_def lift {r : R → R → Prop} :
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_applyₓ'. -/
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
-    lift ⟨f, w⟩ (mkRingHom r x) = f x :=
-  by
-  simp_rw [lift, mk_ring_hom]
-  rfl
+    lift ⟨f, w⟩ (mkRingHom r x) = f x := by simp_rw [lift, mk_ring_hom]; rfl
 #align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_apply
 
 /- warning: ring_quot.lift_unique -> RingQuot.lift_unique is a dubious translation:
@@ -591,21 +506,14 @@ theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_unique RingQuot.lift_uniqueₓ'. -/
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
-    (g : RingQuot r →+* T) (h : g.comp (mkRingHom r) = f) : g = lift ⟨f, w⟩ :=
-  by
-  ext
-  simp [h]
+    (g : RingQuot r →+* T) (h : g.comp (mkRingHom r) = f) : g = lift ⟨f, w⟩ := by ext; simp [h]
 #align ring_quot.lift_unique RingQuot.lift_unique
 
 /- warning: ring_quot.eq_lift_comp_mk_ring_hom -> RingQuot.eq_lift_comp_mkRingHom is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
-    f =
-      lift
-        ⟨f.comp (mkRingHom r), fun x y h => by
-          dsimp
-          rw [mk_ring_hom_rel h]⟩ :=
+    f = lift ⟨f.comp (mkRingHom r), fun x y h => by dsimp; rw [mk_ring_hom_rel h]⟩ :=
   by
   conv_lhs => rw [← lift.apply_symm_apply f]
   rw [lift]
@@ -662,10 +570,8 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
         rw [← sub_eq_iff_eq_add] at su
         rw [← su, RingHom.map_sub, mk_ring_hom_rel h, sub_self]
       · simp
-      · intro a b ha hb
-        simp [ha, hb]
-      · intro a x hx
-        simp [hx])
+      · intro a b ha hb; simp [ha, hb]
+      · intro a x hx; simp [hx])
 #align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuot
 
 /- warning: ring_quot.ideal_quotient_to_ring_quot_apply -> RingQuot.idealQuotientToRingQuot_apply is a dubious translation:
@@ -714,12 +620,9 @@ theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
   by
   induction h
   · exact rel.of (hr _ _ h_h)
-  · rw [star_add, star_add]
-    exact rel.add_left h_ih
-  · rw [star_mul, star_mul]
-    exact rel.mul_right h_ih
-  · rw [star_mul, star_mul]
-    exact rel.mul_left h_ih
+  · rw [star_add, star_add]; exact rel.add_left h_ih
+  · rw [star_mul, star_mul]; exact rel.mul_right h_ih
+  · rw [star_mul, star_mul]; exact rel.mul_left h_ih
 #align ring_quot.rel.star RingQuot.Rel.star
 -/
 
@@ -733,11 +636,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_private.Mathlib.Algebra.RingQuot.0.RingQuot.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.star'_quot RingQuot.star'_quotₓ'. -/
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
-    (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ :=
-  by
-  show star' r _ _ = _
-  rw [star']
-  rfl
+    (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := by show star' r _ _ = _;
+  rw [star']; rfl
 #align ring_quot.star'_quot RingQuot.star'_quot
 
 /- warning: ring_quot.star_ring -> RingQuot.starRing is a dubious translation:
@@ -751,15 +651,9 @@ def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
     (hr : ∀ a b, r a b → r (star a) (star b)) : StarRing (RingQuot r)
     where
   unit := star' r hr
-  star_involutive := by
-    rintro ⟨⟨⟩⟩
-    simp [star'_quot]
-  star_mul := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [star'_quot, mul_quot, star_mul]
-  star_add := by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp [star'_quot, add_quot, star_add]
+  star_involutive := by rintro ⟨⟨⟩⟩; simp [star'_quot]
+  star_mul := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, mul_quot, star_mul]
+  star_add := by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩; simp [star'_quot, add_quot, star_add]
 #align ring_quot.star_ring RingQuot.starRing
 
 end StarRing
@@ -777,20 +671,15 @@ Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom R
 /-- The quotient map from an `S`-algebra to its quotient, as a homomorphism of `S`-algebras.
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
-  { mkRingHom s with
-    commutes' := fun r => by
-      simp [mk_ring_hom]
-      rfl }
+  { mkRingHom s with commutes' := fun r => by simp [mk_ring_hom]; rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
 /- warning: ring_quot.mk_alg_hom_coe -> RingQuot.mkAlgHom_coe is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coeₓ'. -/
 @[simp]
-theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s :=
-  by
-  simp_rw [mk_alg_hom, mk_ring_hom]
-  rfl
+theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s := by
+  simp_rw [mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coe
 
 #print RingQuot.mkAlgHom_rel /-
@@ -800,12 +689,8 @@ theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s
 -/
 
 #print RingQuot.mkAlgHom_surjective /-
-theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) :=
-  by
-  dsimp [mk_alg_hom, mk_ring_hom]
-  rintro ⟨⟨a⟩⟩
-  use a
-  rfl
+theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
+  dsimp [mk_alg_hom, mk_ring_hom]; rintro ⟨⟨a⟩⟩; use a; rfl
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective
 -/
 
@@ -845,45 +730,28 @@ irreducible_def liftAlgHom {s : A → A → Prop} :
               case mul_right _ _ _ _ r' => simp [r'])
             x.toQuot
         map_zero' := by simp [← zero_quot, f.map_zero]
-        map_add' := by
-          rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩
-          simp [add_quot, f.map_add x y]
+        map_add' := by rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩; simp [add_quot, f.map_add x y]
         map_one' := by simp [← one_quot, f.map_one]
-        map_mul' := by
-          rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩
-          simp [mul_quot, f.map_mul x y]
-        commutes' := by
-          rintro x
-          simp [← one_quot, smul_quot, Algebra.algebraMap_eq_smul_one] }
-    invFun := fun F =>
-      ⟨F.comp (mkAlgHom S s), fun _ _ h => by
-        dsimp
-        erw [mk_alg_hom_rel S h]⟩
-    left_inv := fun f => by
-      ext
-      simp [mk_alg_hom, mk_ring_hom]
-    right_inv := fun F => by
-      ext
-      simp [mk_alg_hom, mk_ring_hom] }
+        map_mul' := by rintro ⟨⟨x⟩⟩ ⟨⟨y⟩⟩; simp [mul_quot, f.map_mul x y]
+        commutes' := by rintro x; simp [← one_quot, smul_quot, Algebra.algebraMap_eq_smul_one] }
+    invFun := fun F => ⟨F.comp (mkAlgHom S s), fun _ _ h => by dsimp; erw [mk_alg_hom_rel S h]⟩
+    left_inv := fun f => by ext; simp [mk_alg_hom, mk_ring_hom]
+    right_inv := fun F => by ext; simp [mk_alg_hom, mk_ring_hom] }
 #align ring_quot.lift_alg_hom RingQuot.liftAlgHom
 -/
 
 #print RingQuot.liftAlgHom_mkAlgHom_apply /-
 @[simp]
 theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
-    (w : ∀ ⦃x y⦄, s x y → f x = f y) (x) : (liftAlgHom S ⟨f, w⟩) ((mkAlgHom S s) x) = f x :=
-  by
-  simp_rw [lift_alg_hom, mk_alg_hom, mk_ring_hom]
-  rfl
+    (w : ∀ ⦃x y⦄, s x y → f x = f y) (x) : (liftAlgHom S ⟨f, w⟩) ((mkAlgHom S s) x) = f x := by
+  simp_rw [lift_alg_hom, mk_alg_hom, mk_ring_hom]; rfl
 #align ring_quot.lift_alg_hom_mk_alg_hom_apply RingQuot.liftAlgHom_mkAlgHom_apply
 -/
 
 #print RingQuot.liftAlgHom_unique /-
 -- note this is essentially `(lift_alg_hom S).symm_apply_eq.mp h`
 theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ ⦃x y⦄, s x y → f x = f y)
-    (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ :=
-  by
-  ext
+    (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ := by ext;
   simp [h]
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
 -/
@@ -892,11 +760,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 <too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
-    f =
-      liftAlgHom S
-        ⟨f.comp (mkAlgHom S s), fun x y h => by
-          dsimp
-          erw [mk_alg_hom_rel S h]⟩ :=
+    f = liftAlgHom S ⟨f.comp (mkAlgHom S s), fun x y h => by dsimp; erw [mk_alg_hom_rel S h]⟩ :=
   by
   conv_lhs => rw [← (lift_alg_hom S).apply_symm_apply f]
   rw [lift_alg_hom]

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

@@ -48,10 +48,7 @@ instance (c : RingCon A) : Algebra S c.Quotient
   smul_def' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
 
 /- warning: ring_con.coe_algebra_map -> RingCon.coe_algebraMap is a dubious translation:
-lean 3 declaration is
-  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (HasLiftT.mk.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (CoeTCₓ.coe.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.hasCoeT.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (fun (_x : RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) => S -> (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c)) (RingHom.hasCoeToFun.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) _inst_2 (RingCon.Quotient.semiring.{u2} A _inst_3 c) (RingCon.Quotient.algebra.{u1, u2} S _inst_2 A _inst_3 _inst_4 c)) s)
-but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.toQuotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)) (RingHom.instRingHomClassRingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)))))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _inst_2 (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c) (RingCon.instAlgebraQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMulInstSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u1, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 _inst_4 c)) s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_con.coe_algebra_map RingCon.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
@@ -214,32 +211,25 @@ variable (r : R → R → Prop)
 
 private irreducible_def nat_cast (n : ℕ) : RingQuot r :=
   ⟨Quot.mk _ n⟩
-#align ring_quot.nat_cast ring_quot.nat_cast
 
 private irreducible_def zero : RingQuot r :=
   ⟨Quot.mk _ 0⟩
-#align ring_quot.zero ring_quot.zero
 
 private irreducible_def one : RingQuot r :=
   ⟨Quot.mk _ 1⟩
-#align ring_quot.one ring_quot.one
 
 private irreducible_def add : RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ (· + ·) Rel.add_right Rel.add_left a b⟩
-#align ring_quot.add ring_quot.add
 
 private irreducible_def mul : RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ (· * ·) Rel.mul_right Rel.mul_left a b⟩
-#align ring_quot.mul ring_quot.mul
 
 private irreducible_def neg {R : Type u₁} [Ring R] (r : R → R → Prop) : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (fun a => -a) Rel.neg a⟩
-#align ring_quot.neg ring_quot.neg
 
 private irreducible_def sub {R : Type u₁} [Ring R] (r : R → R → Prop) :
   RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ Sub.sub Rel.sub_right Rel.sub_left a b⟩
-#align ring_quot.sub ring_quot.sub
 
 private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
   | ⟨a⟩ =>
@@ -253,11 +243,9 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
           · rw [pow_succ, pow_succ]
             simpa only [mul] using congr_arg₂ (fun x y => mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) n_ih)
         a⟩
-#align ring_quot.npow ring_quot.npow
 
 private irreducible_def smul [Algebra S R] (n : S) : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (fun a => n • a) (Rel.smul n) a⟩
-#align ring_quot.smul ring_quot.smul
 
 instance : Zero (RingQuot r) :=
   ⟨zero r⟩
@@ -588,10 +576,7 @@ irreducible_def lift {r : R → R → Prop} :
 #align ring_quot.lift RingQuot.lift
 
 /- warning: ring_quot.lift_mk_ring_hom_apply -> RingQuot.lift_mkRingHom_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (x : R), Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (fun (_x : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_applyₓ'. -/
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
@@ -602,10 +587,7 @@ theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃
 #align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_apply
 
 /- warning: ring_quot.lift_unique -> RingQuot.lift_unique is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_unique RingQuot.lift_uniqueₓ'. -/
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
@@ -616,10 +598,7 @@ theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r
 #align ring_quot.lift_unique RingQuot.lift_unique
 
 /- warning: ring_quot.eq_lift_comp_mk_ring_hom -> RingQuot.eq_lift_comp_mkRingHom is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : RingQuot.{u1} R _inst_1 r) => Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f _a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (rfl.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (rfl.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => congr_arg.{succ u1, succ u2} (RingQuot.{u1} R _inst_1 r) T (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (a : RingQuot.{u1} R _inst_1 r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 r) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f =
@@ -657,10 +636,7 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 
 /- warning: ring_quot.ring_quot_to_ideal_quotient_apply -> RingQuot.ringQuotToIdealQuotient_apply is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
-but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
@@ -693,10 +669,7 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
 #align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuot
 
 /- warning: ring_quot.ideal_quotient_to_ring_quot_apply -> RingQuot.idealQuotientToRingQuot_apply is a dubious translation:
-lean 3 declaration is
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (fun (_x : RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) => (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
-but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
@@ -752,7 +725,6 @@ theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
 
 private irreducible_def star' : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (star : R → R) (Rel.star r hr) a⟩
-#align ring_quot.star' ring_quot.star'
 
 /- warning: ring_quot.star'_quot -> RingQuot.star'_quot is a dubious translation:
 lean 3 declaration is
@@ -812,10 +784,7 @@ irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
 /- warning: ring_quot.mk_alg_hom_coe -> RingQuot.mkAlgHom_coe is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), Eq.{succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (HasLiftT.mk.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (CoeTCₓ.coe.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (RingHom.hasCoeT.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (RingQuot.mkRingHom.{u2} A _inst_3 s)
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), Eq.{succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (RingQuot.mkRingHom.{u2} A _inst_3 s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coeₓ'. -/
 @[simp]
 theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s :=
@@ -920,10 +889,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 -/
 
 /- warning: ring_quot.eq_lift_alg_hom_comp_mk_alg_hom -> RingQuot.eq_liftAlgHom_comp_mkAlgHom is a dubious translation:
-lean 3 declaration is
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{max 1 (succ u2) (succ u3), max 1 (succ u2) (succ u3)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (fun (_x : Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) => (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) -> (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Equiv.hasCoeToFun.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} (RingQuot.{u2} A _inst_3 s) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : RingQuot.{u2} A _inst_3 s) => Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f _a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (rfl.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (rfl.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
-but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f =

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

@@ -923,7 +923,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 lean 3 declaration is
   forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{max 1 (succ u2) (succ u3), max 1 (succ u2) (succ u3)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (fun (_x : Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) => (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) -> (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Equiv.hasCoeToFun.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} (RingQuot.{u2} A _inst_3 s) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : RingQuot.{u2} A _inst_3 s) => Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f _a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (rfl.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (rfl.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
 but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f =

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

@@ -51,7 +51,7 @@ instance (c : RingCon A) : Algebra S c.Quotient
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (HasLiftT.mk.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (CoeTCₓ.coe.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.hasCoeT.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (fun (_x : RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) => S -> (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c)) (RingHom.hasCoeToFun.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) _inst_2 (RingCon.Quotient.semiring.{u2} A _inst_3 c) (RingCon.Quotient.algebra.{u1, u2} S _inst_2 A _inst_3 _inst_4 c)) s)
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.toQuotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)) (RingHom.instRingHomClassRingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)))))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _inst_2 (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c) (RingCon.instAlgebraQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMulInstSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u1, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 _inst_4 c)) s)
+  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.toQuotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)) (RingHom.instRingHomClassRingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c)))))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _inst_2 (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 c) (RingCon.instAlgebraQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMulInstSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u1, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => A) s) _inst_3 _inst_4 c)) s)
 Case conversion may be inaccurate. Consider using '#align ring_con.coe_algebra_map RingCon.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
@@ -508,7 +508,7 @@ irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
 Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_relₓ'. -/
 theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r x = mkRingHom r y := by
   simp [mk_ring_hom, Quot.sound (rel.of w)]
@@ -518,7 +518,7 @@ theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
 Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjectiveₓ'. -/
 theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) :=
   by
@@ -548,7 +548,7 @@ variable {T : Type u₄} [Semiring T]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift RingQuot.liftₓ'. -/
 /-- Any ring homomorphism `f : R →+* T` which respects a relation `r : R → R → Prop`
 factors uniquely through a morphism `ring_quot r →+* T`.
@@ -591,7 +591,7 @@ irreducible_def lift {r : R → R → Prop} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (x : R), Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (fun (_x : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (fun (_x : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_applyₓ'. -/
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
@@ -605,7 +605,7 @@ theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.lift_unique RingQuot.lift_uniqueₓ'. -/
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
@@ -619,7 +619,7 @@ theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : RingQuot.{u1} R _inst_1 r) => Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f _a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (rfl.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (rfl.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => congr_arg.{succ u1, succ u2} (RingQuot.{u1} R _inst_1 r) T (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (a : RingQuot.{u1} R _inst_1 r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 r) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => congr_arg.{succ u1, succ u2} (RingQuot.{u1} R _inst_1 r) T (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (a : RingQuot.{u1} R _inst_1 r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} R _inst_1 r) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f =
@@ -660,7 +660,7 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
@@ -696,7 +696,7 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (fun (_x : RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) => (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
@@ -923,7 +923,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 lean 3 declaration is
   forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{max 1 (succ u2) (succ u3), max 1 (succ u2) (succ u3)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (fun (_x : Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) => (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) -> (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Equiv.hasCoeToFun.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} (RingQuot.{u2} A _inst_3 s) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : RingQuot.{u2} A _inst_3 s) => Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f _a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (rfl.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (rfl.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
 but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f =

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

@@ -653,7 +653,7 @@ Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift
     ⟨Ideal.Quotient.mk (Ideal.ofRel r), fun x y h =>
-      Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr fun p w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
+      Ideal.Quotient.eq.2 <| Submodule.mem_sInf.mpr fun p w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 
 /- warning: ring_quot.ring_quot_to_ideal_quotient_apply -> RingQuot.ringQuotToIdealQuotient_apply is a dubious translation:

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

@@ -647,7 +647,7 @@ variable {B : Type u₁} [CommRing B]
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotientₓ'. -/
 /-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
@@ -660,7 +660,7 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
@@ -674,7 +674,7 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuotₓ'. -/
 /-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
@@ -696,7 +696,7 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (fun (_x : RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) => (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
@@ -708,7 +708,7 @@ theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Distrib.toHasMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasAdd.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))))) (Distrib.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.instMulRingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocRing.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.instAddRingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Distrib.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (RingQuot.instMulRingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (NonUnitalNonAssocRing.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)))))) (RingQuot.instAddRingQuot.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r) (Distrib.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} B _inst_6) (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_6)) r))))))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_equiv_ideal_quotient RingQuot.ringQuotEquivIdealQuotientₓ'. -/
 /-- The ring equivalence between `ring_quot r` and `(ideal.of_rel r).quotient`
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -756,7 +756,7 @@ private irreducible_def star' : RingQuot r → RingQuot r
 
 /- warning: ring_quot.star'_quot -> RingQuot.star'_quot is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.4149469211.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.2156597245.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_private.Mathlib.Algebra.RingQuot.0.RingQuot.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.star'_quot RingQuot.star'_quotₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -647,7 +647,7 @@ variable {B : Type u₁} [CommRing B]
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotientₓ'. -/
 /-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
@@ -660,7 +660,7 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
@@ -674,7 +674,7 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuotₓ'. -/
 /-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
@@ -696,7 +696,7 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
 lean 3 declaration is
   forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (fun (_x : RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) => (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
 but is expected to have type
-  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instRing.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
 Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.ring_quot
-! leanprover-community/mathlib commit e5820f6c8fcf1b75bcd7738ae4da1c5896191f72
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! 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.Ideal.Quotient
 /-!
 # Quotients of non-commutative rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Unfortunately, ideals have only been developed in the commutative case as `ideal`,
 and it's not immediately clear how one should formalise ideals in the non-commutative case.
 
@@ -753,7 +756,7 @@ private irreducible_def star' : RingQuot r → RingQuot r
 
 /- warning: ring_quot.star'_quot -> RingQuot.star'_quot is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.2632819077.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.4149469211.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_private.Mathlib.Algebra.RingQuot.0.RingQuot.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
 Case conversion may be inaccurate. Consider using '#align ring_quot.star'_quot RingQuot.star'_quotₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

@@ -616,7 +616,7 @@ theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : RingQuot.{u1} R _inst_1 r) => Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f _a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (rfl.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (rfl.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id.{0} (Eq.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) => Eq.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f _a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.refl.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (Eq.refl.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => congr_arg.{succ u1, succ u2} (RingQuot.{u1} R _inst_1 r) T (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (a : RingQuot.{u1} R _inst_1 r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 r) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f =
@@ -920,7 +920,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 lean 3 declaration is
   forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{max 1 (succ u2) (succ u3), max 1 (succ u2) (succ u3)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (fun (_x : Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) => (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) -> (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Equiv.hasCoeToFun.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} (RingQuot.{u2} A _inst_3 s) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : RingQuot.{u2} A _inst_3 s) => Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f _a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (rfl.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (rfl.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
 but is expected to have type
-  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id.{0} (Eq.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) x) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) x) => Eq.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f _a) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.refl.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (Eq.refl.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 (fun (x : A) (y : A) => s x y)) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 (fun (x : A) (y : A) => s x y)) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 (fun (x : A) (y : A) => s x y)) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => congr_arg.{succ u2, succ u3} (RingQuot.{u2} A _inst_3 s) B (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => RingQuot.{u2} A _inst_3 s) a) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (RingHom.instRingHomClassRingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (a : RingQuot.{u2} A _inst_3 s) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : RingQuot.{u2} A _inst_3 s) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))))
 Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f =

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

@@ -44,6 +44,12 @@ instance (c : RingCon A) : Algebra S c.Quotient
   commutes' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.commutes _ _
   smul_def' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
 
+/- warning: ring_con.coe_algebra_map -> RingCon.coe_algebraMap is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (HasLiftT.mk.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (CoeTCₓ.coe.{succ u2, succ u2} A (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.hasCoeT.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => S -> A) (RingHom.hasCoeToFun.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (fun (_x : RingHom.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) => S -> (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c)) (RingHom.hasCoeToFun.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) (RingCon.Quotient.semiring.{u2} A _inst_3 c))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) c) _inst_2 (RingCon.Quotient.semiring.{u2} A _inst_3 c) (RingCon.Quotient.algebra.{u1, u2} S _inst_2 A _inst_3 _inst_4 c)) s)
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (c : RingCon.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (s : S), Eq.{succ u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.toQuotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} S A (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} S A _inst_2 _inst_3 _inst_4) s)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c))) S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)) (RingHom.instRingHomClassRingHom.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{u2} (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c)))))) (algebraMap.{u1, u2} S (RingCon.Quotient.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) c) _inst_2 (RingCon.instSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 c) (RingCon.instAlgebraQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMulInstSemiringQuotientToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToMul.{u1, u2} S _inst_2 ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => A) s) _inst_3 _inst_4 c)) s)
+Case conversion may be inaccurate. Consider using '#align ring_con.coe_algebra_map RingCon.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
     (↑(algebraMap S A s) : c.Quotient) = algebraMap S _ s :=
@@ -54,6 +60,7 @@ end RingCon
 
 namespace RingQuot
 
+#print RingQuot.Rel /-
 /-- Given an arbitrary relation `r` on a ring, we strengthen it to a relation `rel r`,
 such that the equivalence relation generated by `rel r` has `x ~ y` if and only if
 `x - y` is in the ideal generated by elements `a - b` such that `r a b`.
@@ -64,29 +71,62 @@ inductive Rel (r : R → R → Prop) : R → R → Prop
   | mul_left ⦃a b c⦄ : Rel a b → Rel (a * c) (b * c)
   | mul_right ⦃a b c⦄ : Rel b c → Rel (a * b) (a * c)
 #align ring_quot.rel RingQuot.Rel
+-/
 
+/- warning: ring_quot.rel.add_right -> RingQuot.Rel.add_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R _inst_1 r b c) -> (RingQuot.Rel.{u1} R _inst_1 r (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a c))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R _inst_1 r b c) -> (RingQuot.Rel.{u1} R _inst_1 r (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a c))
+Case conversion may be inaccurate. Consider using '#align ring_quot.rel.add_right RingQuot.Rel.add_rightₓ'. -/
 theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : Rel r (a + b) (a + c) :=
   by
   rw [add_comm a b, add_comm a c]
   exact rel.add_left h
 #align ring_quot.rel.add_right RingQuot.Rel.add_right
 
+/- warning: ring_quot.rel.neg -> RingQuot.Rel.neg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) a) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) b))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) a) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) b))
+Case conversion may be inaccurate. Consider using '#align ring_quot.rel.neg RingQuot.Rel.negₓ'. -/
 theorem Rel.neg {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b : R⦄ (h : Rel r a b) :
     Rel r (-a) (-b) := by simp only [neg_eq_neg_one_mul a, neg_eq_neg_one_mul b, rel.mul_right h]
 #align ring_quot.rel.neg RingQuot.Rel.neg
 
+/- warning: ring_quot.rel.sub_left -> RingQuot.Rel.sub_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a c) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) b c))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r a b) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a c) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) b c))
+Case conversion may be inaccurate. Consider using '#align ring_quot.rel.sub_left RingQuot.Rel.sub_leftₓ'. -/
 theorem Rel.sub_left {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r a b) :
     Rel r (a - c) (b - c) := by simp only [sub_eq_add_neg, h.add_left]
 #align ring_quot.rel.sub_left RingQuot.Rel.sub_left
 
+/- warning: ring_quot.rel.sub_right -> RingQuot.Rel.sub_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r b c) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a b) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a c))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] {r : R -> R -> Prop} {{a : R}} {{b : R}} {{c : R}}, (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r b c) -> (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a b) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a c))
+Case conversion may be inaccurate. Consider using '#align ring_quot.rel.sub_right RingQuot.Rel.sub_rightₓ'. -/
 theorem Rel.sub_right {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) :
     Rel r (a - b) (a - c) := by simp only [sub_eq_add_neg, h.neg.add_right]
 #align ring_quot.rel.sub_right RingQuot.Rel.sub_right
 
+#print RingQuot.Rel.smul /-
 theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) : Rel r (k • a) (k • b) := by
   simp only [Algebra.smul_def, rel.mul_right h]
 #align ring_quot.rel.smul RingQuot.Rel.smul
+-/
 
+/- warning: ring_quot.ring_con -> RingQuot.ringCon is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (R -> R -> Prop) -> (RingCon.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (R -> R -> Prop) -> (RingCon.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_con RingQuot.ringConₓ'. -/
 /-- `eqv_gen (ring_quot.rel r)` is a ring congruence. -/
 def ringCon (r : R → R → Prop) : RingCon R
     where
@@ -126,6 +166,12 @@ def ringCon (r : R → R → Prop) : RingCon R
     · exact (ihcd' _ _ hcd).trans _ _ _ (ihde' _ _ <| EqvGen.refl _)
 #align ring_quot.ring_con RingQuot.ringCon
 
+/- warning: ring_quot.eqv_gen_rel_eq -> RingQuot.eqvGen_rel_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (R -> R -> Prop) (EqvGen.{u1} R (RingQuot.Rel.{u1} R _inst_1 r)) (RingConGen.Rel.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) r)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (R -> R -> Prop) (EqvGen.{u1} R (RingQuot.Rel.{u1} R _inst_1 r)) (RingConGen.Rel.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) r)
+Case conversion may be inaccurate. Consider using '#align ring_quot.eqv_gen_rel_eq RingQuot.eqvGen_rel_eqₓ'. -/
 theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r :=
   by
   ext (x₁ x₂)
@@ -152,10 +198,12 @@ theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r
 
 end RingQuot
 
+#print RingQuot /-
 /-- The quotient of a ring by an arbitrary relation. -/
 structure RingQuot (r : R → R → Prop) where
   toQuot : Quot (RingQuot.Rel r)
 #align ring_quot RingQuot
+-/
 
 namespace RingQuot
 
@@ -232,14 +280,32 @@ instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Sub (RingQuot r) :=
 instance [Algebra S R] : SMul S (RingQuot r) :=
   ⟨smul r⟩
 
+/- warning: ring_quot.zero_quot -> RingQuot.zero_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 0 (OfNat.mk.{u1} (RingQuot.{u1} R _inst_1 r) 0 (Zero.zero.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasZero.{u1} R _inst_1 r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 0 (Zero.toOfNat0.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instZeroRingQuot.{u1} R _inst_1 r)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.zero_quot RingQuot.zero_quotₓ'. -/
 theorem zero_quot : (⟨Quot.mk _ 0⟩ : RingQuot r) = 0 :=
   show _ = zero r by rw [zero]
 #align ring_quot.zero_quot RingQuot.zero_quot
 
+/- warning: ring_quot.one_quot -> RingQuot.one_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 1 (OfNat.mk.{u1} (RingQuot.{u1} R _inst_1 r) 1 (One.one.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasOne.{u1} R _inst_1 r))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (RingQuot.{u1} R _inst_1 r) 1 (One.toOfNat1.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instOneRingQuot.{u1} R _inst_1 r)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.one_quot RingQuot.one_quotₓ'. -/
 theorem one_quot : (⟨Quot.mk _ 1⟩ : RingQuot r) = 1 :=
   show _ = one r by rw [one]
 #align ring_quot.one_quot RingQuot.one_quot
 
+/- warning: ring_quot.add_quot -> RingQuot.add_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHAdd.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasAdd.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHAdd.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instAddRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.add_quot RingQuot.add_quotₓ'. -/
 theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a + b)⟩ :=
   by
   show add r _ _ = _
@@ -247,6 +313,12 @@ theorem add_quot {a b} : (⟨Quot.mk _ a⟩ + ⟨Quot.mk _ b⟩ : RingQuot r) =
   rfl
 #align ring_quot.add_quot RingQuot.add_quot
 
+/- warning: ring_quot.mul_quot -> RingQuot.mul_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHMul.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.hasMul.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) a b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHMul.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instMulRingQuot.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) b))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) a b)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.mul_quot RingQuot.mul_quotₓ'. -/
 theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a * b)⟩ :=
   by
   show mul r _ _ = _
@@ -254,12 +326,24 @@ theorem mul_quot {a b} : (⟨Quot.mk _ a⟩ * ⟨Quot.mk _ b⟩ : RingQuot r) =
   rfl
 #align ring_quot.mul_quot RingQuot.mul_quot
 
+/- warning: ring_quot.pow_quot -> RingQuot.pow_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {n : Nat}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.{u1} R _inst_1 r) (instHPow.{u1, 0} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.Nat.hasPow.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) n) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) a n)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) {a : R} {n : Nat}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.{u1} R _inst_1 r) (instHPow.{u1, 0} (RingQuot.{u1} R _inst_1 r) Nat (RingQuot.instPowRingQuotNat.{u1} R _inst_1 r)) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a)) n) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) a n)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.pow_quot RingQuot.pow_quotₓ'. -/
 theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.mk _ (a ^ n)⟩ :=
   by
   show npow r _ _ = _
   rw [npow]
 #align ring_quot.pow_quot RingQuot.pow_quot
 
+/- warning: ring_quot.neg_quot -> RingQuot.neg_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.hasNeg.{u1} R _inst_5 r) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5))))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instNegRingQuotToSemiring.{u1} R _inst_5 r) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (Neg.neg.{u1} R (Ring.toNeg.{u1} R _inst_5) a)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.neg_quot RingQuot.neg_quotₓ'. -/
 theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
     (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ :=
   by
@@ -268,6 +352,12 @@ theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
   rfl
 #align ring_quot.neg_quot RingQuot.neg_quot
 
+/- warning: ring_quot.sub_quot -> RingQuot.sub_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (instHSub.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.hasSub.{u1} R _inst_5 r)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) b))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_5)))))) a b)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : Ring.{u1} R] (r : R -> R -> Prop) {a : R} {b : R}, Eq.{succ u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (instHSub.{u1} (RingQuot.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (RingQuot.instSubRingQuotToSemiring.{u1} R _inst_5 r)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) a)) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) b))) (RingQuot.mk.{u1} R (Ring.toSemiring.{u1} R _inst_5) r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R (Ring.toSemiring.{u1} R _inst_5) r) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R _inst_5)) a b)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.sub_quot RingQuot.sub_quotₓ'. -/
 theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
     (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ :=
   by
@@ -276,6 +366,12 @@ theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
   rfl
 #align ring_quot.sub_quot RingQuot.sub_quot
 
+/- warning: ring_quot.smul_quot -> RingQuot.smul_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (r : R -> R -> Prop) [_inst_5 : Algebra.{u2, u1} S R _inst_2 _inst_1] {n : S} {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (SMul.smul.{u2, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.hasSmul.{u1, u2} R _inst_1 S _inst_2 r _inst_5) n (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (SMul.smul.{u2, u1} S R (SMulZeroClass.toHasSmul.{u2, u1} S R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (SMulWithZero.toSmulZeroClass.{u2, u1} S R (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} S R (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Module.toMulActionWithZero.{u2, u1} S R (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Algebra.toModule.{u2, u1} S R _inst_2 _inst_1 _inst_5))))) n a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} [_inst_2 : CommSemiring.{u2} S] (r : R -> R -> Prop) [_inst_5 : Algebra.{u2, u1} S R _inst_2 _inst_1] {n : S} {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.{u1} R _inst_1 r) (instHSMul.{u2, u1} S (RingQuot.{u1} R _inst_1 r) (RingQuot.instSMulRingQuot.{u1, u2} R _inst_1 S _inst_2 r _inst_5)) n (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (HSMul.hSMul.{u2, u1, u1} S R R (instHSMul.{u2, u1} S R (Algebra.toSMul.{u2, u1} S R _inst_2 _inst_1 _inst_5)) n a)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.smul_quot RingQuot.smul_quotₓ'. -/
 theorem smul_quot [Algebra S R] {n : S} {a : R} :
     (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ :=
   by
@@ -389,6 +485,12 @@ instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r)
     rintro ⟨⟨a⟩⟩
     simp [smul_quot, Algebra.smul_def, mul_quot]
 
+/- warning: ring_quot.mk_ring_hom -> RingQuot.mkRingHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom RingQuot.mkRingHomₓ'. -/
 /-- The quotient map from a ring to its quotient, as a homomorphism of rings.
 -/
 irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
@@ -399,10 +501,22 @@ irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
     map_add' := by simp [add_quot] }
 #align ring_quot.mk_ring_hom RingQuot.mkRingHom
 
+/- warning: ring_quot.mk_ring_hom_rel -> RingQuot.mkRingHom_rel is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {r : R -> R -> Prop} {x : R} {y : R}, (r x y) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))
+Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_relₓ'. -/
 theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r x = mkRingHom r y := by
   simp [mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_rel
 
+/- warning: ring_quot.mk_ring_hom_surjective -> RingQuot.mkRingHom_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop), Function.Surjective.{succ u1, succ u1} R (RingQuot.{u1} R _inst_1 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r))
+Case conversion may be inaccurate. Consider using '#align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjectiveₓ'. -/
 theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) :=
   by
   dsimp [mk_ring_hom]
@@ -410,6 +524,12 @@ theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRin
   simp
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective
 
+/- warning: ring_quot.ring_quot_ext -> RingQuot.ringQuot_ext is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r))) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f g)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r))) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f g)
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_ext RingQuot.ringQuot_extₓ'. -/
 @[ext]
 theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g : RingQuot r →+* T)
     (w : f.comp (mkRingHom r) = g.comp (mkRingHom r)) : f = g :=
@@ -421,6 +541,12 @@ theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g :
 
 variable {T : Type u₄} [Semiring T]
 
+/- warning: ring_quot.lift -> RingQuot.lift is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop}, Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))
+Case conversion may be inaccurate. Consider using '#align ring_quot.lift RingQuot.liftₓ'. -/
 /-- Any ring homomorphism `f : R →+* T` which respects a relation `r : R → R → Prop`
 factors uniquely through a morphism `ring_quot r →+* T`.
 -/
@@ -458,6 +584,12 @@ irreducible_def lift {r : R → R → Prop} :
       simp [mk_ring_hom] }
 #align ring_quot.lift RingQuot.lift
 
+/- warning: ring_quot.lift_mk_ring_hom_apply -> RingQuot.lift_mkRingHom_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (x : R), Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (x : R), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (fun (_x : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x)
+Case conversion may be inaccurate. Consider using '#align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_applyₓ'. -/
 @[simp]
 theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y) (x) :
     lift ⟨f, w⟩ (mkRingHom r x) = f x :=
@@ -466,6 +598,12 @@ theorem lift_mkRingHom_apply (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃
   rfl
 #align ring_quot.lift_mk_ring_hom_apply RingQuot.lift_mkRingHom_apply
 
+/- warning: ring_quot.lift_unique -> RingQuot.lift_unique is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.semiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) f w)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) {r : R -> R -> Prop} (w : forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (g : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) g (RingQuot.mkRingHom.{u1} R _inst_1 r)) f) -> (Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) g (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 (fun (x : R) (y : R) => r x y)) (RingQuot.instSemiring.{u1} R _inst_1 (fun (x : R) (y : R) => r x y))) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 (fun (x : R) (y : R) => r x y)) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) f w)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.lift_unique RingQuot.lift_uniqueₓ'. -/
 -- note this is essentially `lift.symm_apply_eq.mp h`
 theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r x y → f x = f y)
     (g : RingQuot r →+* T) (h : g.comp (mkRingHom r) = f) : g = lift ⟨f, w⟩ :=
@@ -474,6 +612,12 @@ theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r
   simp [h]
 #align ring_quot.lift_unique RingQuot.lift_unique
 
+/- warning: ring_quot.eq_lift_comp_mk_ring_hom -> RingQuot.eq_lift_comp_mkRingHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{max 1 (succ u1) (succ u2), max 1 (succ u1) (succ u2)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (fun (_x : Equiv.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) => (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) -> (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Equiv.hasCoeToFun.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => R -> T) (RingHom.hasCoeToFun.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} (RingQuot.{u1} R _inst_1 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : RingQuot.{u1} R _inst_1 r) => Eq.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f _a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (rfl.{1} Prop (Eq.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (rfl.{succ u2} T (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (_x : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => (RingQuot.{u1} R _inst_1 r) -> T) (RingHom.hasCoeToFun.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (fun (_x : RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) => R -> (RingQuot.{u1} R _inst_1 r)) (RingHom.hasCoeToFun.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.semiring.{u1} R _inst_1 r))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {T : Type.{u2}} [_inst_5 : Semiring.{u2} T] {r : R -> R -> Prop} (f : RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)), Eq.{max (succ u1) (succ u2)} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) f (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max 1 (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (fun (_x : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) a) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) => RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Subtype.{max (succ u1) (succ u2)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y)))) (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (RingQuot.lift.{u1, u2} R _inst_1 T _inst_5 r) (Subtype.mk.{max (succ u2) (succ u1)} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (fun (f : RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) => forall {{x : R}} {{y : R}}, (r x y) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f y))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) (fun (x : R) (y : R) (h : r x y) => id.{0} (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) x) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => T) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} R T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) (RingHom.comp.{u1, u1, u2} R (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) f (RingQuot.mkRingHom.{u1} R _inst_1 r)) y)) (Eq.mpr.{0} (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (id.{0} (Eq.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.ndrec.{0, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) x) => Eq.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y))) (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f _a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (Eq.refl.{1} Prop (Eq.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => RingQuot.{u1} R _inst_1 r) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y) (RingQuot.mkRingHom_rel.{u1} R _inst_1 r x y h))) (Eq.refl.{succ u2} T (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) (fun (_x : RingQuot.{u1} R _inst_1 r) => T) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalNonAssocSemiring.toMul.{u2} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} T (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5)) (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5) (RingHom.instRingHomClassRingHom.{u1, u2} (RingQuot.{u1} R _inst_1 r) T (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (Semiring.toNonAssocSemiring.{u2} T _inst_5))))) f (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => RingQuot.{u1} R _inst_1 r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r))) R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)) (RingHom.instRingHomClassRingHom.{u1, u1} R (RingQuot.{u1} R _inst_1 r) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} R _inst_1 r) (RingQuot.instSemiring.{u1} R _inst_1 r)))))) (RingQuot.mkRingHom.{u1} R _inst_1 r) y)))))))
+Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_comp_mk_ring_hom RingQuot.eq_lift_comp_mkRingHomₓ'. -/
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
     f =
       lift
@@ -496,6 +640,12 @@ agrees with the quotient by the appropriate ideal.
 
 variable {B : Type u₁} [CommRing B]
 
+/- warning: ring_quot.ring_quot_to_ideal_quotient -> RingQuot.ringQuotToIdealQuotient is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
+but is expected to have type
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotientₓ'. -/
 /-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift
@@ -503,6 +653,12 @@ def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Idea
       Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr fun p w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 
+/- warning: ring_quot.ring_quot_to_ideal_quotient_apply -> RingQuot.ringQuotToIdealQuotient_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
+but is expected to have type
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (fun (_x : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (RingQuot.ringQuotToIdealQuotient.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_applyₓ'. -/
 @[simp]
 theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
     ringQuotToIdealQuotient r (mkRingHom r x) = Ideal.Quotient.mk _ x :=
@@ -511,6 +667,12 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
   rfl
 #align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_apply
 
+/- warning: ring_quot.ideal_quotient_to_ring_quot -> RingQuot.idealQuotientToRingQuot is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))
+but is expected to have type
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuotₓ'. -/
 /-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
   Ideal.Quotient.lift (Ideal.ofRel r) (mkRingHom r)
@@ -527,12 +689,24 @@ def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* R
         simp [hx])
 #align ring_quot.ideal_quotient_to_ring_quot RingQuot.idealQuotientToRingQuot
 
+/- warning: ring_quot.ideal_quotient_to_ring_quot_apply -> RingQuot.idealQuotientToRingQuot_apply is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (fun (_x : RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) => (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (fun (_x : RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) => B -> (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHom.hasCoeToFun.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (fun (_x : RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) => B -> (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.hasCoeToFun.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.semiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
+but is expected to have type
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop) (x : B), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (a : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (fun (_x : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r)))) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))) (RingHom.instRingHomClassRingHom.{u1, u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.Ring.{u1} B (CommRing.toRing.{u1} B _inst_6) r))))))) (RingQuot.idealQuotientToRingQuot.{u1} B _inst_6 r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))) (RingHom.instRingHomClassRingHom.{u1, u1} B (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} B (Ring.toNonAssocRing.{u1} B (CommRing.toRing.{u1} B _inst_6))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))) (Ideal.Quotient.mk.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : B) => RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))))) (NonUnitalNonAssocSemiring.toMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))) B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingHom.instRingHomClassRingHom.{u1, u1} B (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Semiring.toNonAssocSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Semiring.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.instSemiring.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.mkRingHom.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) x)
+Case conversion may be inaccurate. Consider using '#align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_applyₓ'. -/
 @[simp]
 theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
     idealQuotientToRingQuot r (Ideal.Quotient.mk _ x) = mkRingHom r x :=
   rfl
 #align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_apply
 
+/- warning: ring_quot.ring_quot_equiv_ideal_quotient -> RingQuot.ringQuotEquivIdealQuotient is a dubious translation:
+lean 3 declaration is
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Distrib.toHasMul.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasAdd.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocSemiring.toDistrib.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonAssocRing.toNonAssocSemiring.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Ring.toNonAssocRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (CommRing.toRing.{u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (RingQuot.commRing.{u1} B _inst_6 r))))))) (Distrib.toHasMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))))) (Distrib.toHasAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.hasQuotient.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))
+but is expected to have type
+  forall {B : Type.{u1}} [_inst_6 : CommRing.{u1} B] (r : B -> B -> Prop), RingEquiv.{u1, u1} (RingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (RingQuot.instMulRingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (NonUnitalNonAssocRing.toMul.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)))))) (RingQuot.instAddRingQuot.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r) (Distrib.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} B (Ideal.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} B _inst_6) (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r)) (Ideal.Quotient.commRing.{u1} B _inst_6 (Ideal.ofRel.{u1} B (Ring.toSemiring.{u1} B (CommRing.toRing.{u1} B _inst_6)) r))))))))
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_equiv_ideal_quotient RingQuot.ringQuotEquivIdealQuotientₓ'. -/
 /-- The ring equivalence between `ring_quot r` and `(ideal.of_rel r).quotient`
 -/
 def ringQuotEquivIdealQuotient (r : B → B → Prop) : RingQuot r ≃+* B ⧸ Ideal.ofRel r :=
@@ -559,6 +733,7 @@ variable [StarRing R] (r) (hr : ∀ a b, r a b → r (star a) (star b))
 
 include hr
 
+#print RingQuot.Rel.star /-
 theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
   by
   induction h
@@ -570,11 +745,18 @@ theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) :=
   · rw [star_mul, star_mul]
     exact rel.mul_left h_ih
 #align ring_quot.rel.star RingQuot.Rel.star
+-/
 
 private irreducible_def star' : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (star : R → R) (Rel.star r hr) a⟩
 #align ring_quot.star' ring_quot.star'
 
+/- warning: ring_quot.star'_quot -> RingQuot.star'_quot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_Private.2632819077.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R -> R -> Prop) [_inst_6 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] (hr : forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) b))) {a : R}, Eq.{succ u1} (RingQuot.{u1} R _inst_1 r) (_private.Mathlib.Algebra.RingQuot.0.RingQuot.star'.{u1} R _inst_1 r _inst_6 hr (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) a))) (RingQuot.mk.{u1} R _inst_1 r (Quot.mk.{succ u1} R (RingQuot.Rel.{u1} R _inst_1 r) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_6))) a)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.star'_quot RingQuot.star'_quotₓ'. -/
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
     (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ :=
   by
@@ -583,6 +765,12 @@ theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
   rfl
 #align ring_quot.star'_quot RingQuot.star'_quot
 
+/- warning: ring_quot.star_ring -> RingQuot.starRing is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_7 : Semiring.{u1} R] [_inst_8 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)] (r : R -> R -> Prop), (forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) a) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) b))) -> (StarRing.{u1} (RingQuot.{u1} R _inst_7 r) (Semiring.toNonUnitalSemiring.{u1} (RingQuot.{u1} R _inst_7 r) (RingQuot.semiring.{u1} R _inst_7 r)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_7 : Semiring.{u1} R] [_inst_8 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7)] (r : R -> R -> Prop), (forall (a : R) (b : R), (r a b) -> (r (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) a) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_7)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_7) _inst_8))) b))) -> (StarRing.{u1} (RingQuot.{u1} R _inst_7 r) (Semiring.toNonUnitalSemiring.{u1} (RingQuot.{u1} R _inst_7 r) (RingQuot.instSemiring.{u1} R _inst_7 r)))
+Case conversion may be inaccurate. Consider using '#align ring_quot.star_ring RingQuot.starRingₓ'. -/
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/
 def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
     (hr : ∀ a b, r a b → r (star a) (star b)) : StarRing (RingQuot r)
@@ -605,6 +793,12 @@ section Algebra
 
 variable (S)
 
+/- warning: ring_quot.mk_alg_hom -> RingQuot.mkAlgHom is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)
+Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom RingQuot.mkAlgHomₓ'. -/
 /-- The quotient map from an `S`-algebra to its quotient, as a homomorphism of `S`-algebras.
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
@@ -614,6 +808,12 @@ irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
       rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
+/- warning: ring_quot.mk_alg_hom_coe -> RingQuot.mkAlgHom_coe is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), Eq.{succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (HasLiftT.mk.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (CoeTCₓ.coe.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s))) (RingHom.hasCoeT.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.semiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (RingQuot.mkRingHom.{u2} A _inst_3 s)
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] (s : A -> A -> Prop), Eq.{succ u2} (RingHom.{u2, u2} A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (RingQuot.mkRingHom.{u2} A _inst_3 s)
+Case conversion may be inaccurate. Consider using '#align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coeₓ'. -/
 @[simp]
 theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s) = mkRingHom s :=
   by
@@ -621,10 +821,13 @@ theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s
   rfl
 #align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coe
 
+#print RingQuot.mkAlgHom_rel /-
 theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s x = mkAlgHom S s y :=
   by simp [mk_alg_hom, mk_ring_hom, Quot.sound (rel.of w)]
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
+-/
 
+#print RingQuot.mkAlgHom_surjective /-
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) :=
   by
   dsimp [mk_alg_hom, mk_ring_hom]
@@ -632,9 +835,16 @@ theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgH
   use a
   rfl
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective
+-/
 
 variable {B : Type u₄} [Semiring B] [Algebra S B]
 
+/- warning: ring_quot.ring_quot_ext' -> RingQuot.ringQuot_ext' is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (g : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 g (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s))) -> (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f g)
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (g : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 g (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s))) -> (Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f g)
+Case conversion may be inaccurate. Consider using '#align ring_quot.ring_quot_ext' RingQuot.ringQuot_ext'ₓ'. -/
 @[ext]
 theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
     (w : f.comp (mkAlgHom S s) = g.comp (mkAlgHom S s)) : f = g :=
@@ -644,6 +854,7 @@ theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
   exact (AlgHom.congr_fun w x : _)
 #align ring_quot.ring_quot_ext' RingQuot.ringQuot_ext'
 
+#print RingQuot.liftAlgHom /-
 /-- Any `S`-algebra homomorphism `f : A →ₐ[S] B` which respects a relation `s : A → A → Prop`
 factors uniquely through a morphism `ring_quot s →ₐ[S]  B`.
 -/
@@ -683,7 +894,9 @@ irreducible_def liftAlgHom {s : A → A → Prop} :
       ext
       simp [mk_alg_hom, mk_ring_hom] }
 #align ring_quot.lift_alg_hom RingQuot.liftAlgHom
+-/
 
+#print RingQuot.liftAlgHom_mkAlgHom_apply /-
 @[simp]
 theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
     (w : ∀ ⦃x y⦄, s x y → f x = f y) (x) : (liftAlgHom S ⟨f, w⟩) ((mkAlgHom S s) x) = f x :=
@@ -691,7 +904,9 @@ theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
   simp_rw [lift_alg_hom, mk_alg_hom, mk_ring_hom]
   rfl
 #align ring_quot.lift_alg_hom_mk_alg_hom_apply RingQuot.liftAlgHom_mkAlgHom_apply
+-/
 
+#print RingQuot.liftAlgHom_unique /-
 -- note this is essentially `(lift_alg_hom S).symm_apply_eq.mp h`
 theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ ⦃x y⦄, s x y → f x = f y)
     (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ :=
@@ -699,7 +914,14 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
   ext
   simp [h]
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
+-/
 
+/- warning: ring_quot.eq_lift_alg_hom_comp_mk_alg_hom -> RingQuot.eq_liftAlgHom_comp_mkAlgHom is a dubious translation:
+lean 3 declaration is
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{max 1 (succ u2) (succ u3), max 1 (succ u2) (succ u3)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (fun (_x : Equiv.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) => (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) -> (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Equiv.hasCoeToFun.{max 1 (succ u2) (succ u3), max (succ u2) (succ u3)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => A -> B) ([anonymous].{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} (RingQuot.{u2} A _inst_3 s) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : RingQuot.{u2} A _inst_3 s) => Eq.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f _a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (rfl.{1} Prop (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (rfl.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (fun (_x : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) => (RingQuot.{u2} A _inst_3 s) -> B) ([anonymous].{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.semiring.{u2} A _inst_3 s) _inst_6 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (fun (_x : AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) => A -> (RingQuot.{u2} A _inst_3 s)) ([anonymous].{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.semiring.{u2} A _inst_3 s) _inst_4 (RingQuot.algebra.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
+but is expected to have type
+  forall (S : Type.{u1}) [_inst_2 : CommSemiring.{u1} S] {A : Type.{u2}} [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} S A _inst_2 _inst_3] {B : Type.{u3}} [_inst_6 : Semiring.{u3} B] [_inst_7 : Algebra.{u1, u3} S B _inst_2 _inst_6] {s : A -> A -> Prop} (f : AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) f (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} (Equiv.{max 1 (succ u2) (succ u3), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (fun (_x : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) => AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (Subtype.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y)))) (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7)) (RingQuot.liftAlgHom.{u1, u2, u3} S _inst_2 A _inst_3 _inst_4 B _inst_6 _inst_7 s) (Subtype.mk.{max (succ u3) (succ u2)} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (fun (f : AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) => forall {{x : A}} {{y : A}}, (s x y) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) f y))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) (fun (x : A) (y : A) (h : s x y) => id.{0} (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) S A B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u2 u3} S A B (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u2 u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7 (AlgHom.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S A B _inst_2 _inst_3 _inst_6 _inst_4 _inst_7))))) (AlgHom.comp.{u1, u2, u2, u3} S A (RingQuot.{u2} A _inst_3 s) B _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 f (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s)) y)) (Eq.mpr.{0} (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (id.{0} (Eq.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.ndrec.{0, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) x) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) x) => Eq.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y))) (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f _a) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (Eq.refl.{1} Prop (Eq.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) x)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => RingQuot.{u2} A _inst_3 s) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y) (RingQuot.mkAlgHom_rel.{u1, u2} S _inst_2 A _inst_3 _inst_4 s x y h))) (Eq.refl.{succ u3} B (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (RingQuot.{u2} A _inst_3 s) (fun (_x : RingQuot.{u2} A _inst_3 s) => B) (SMulHomClass.toFunLike.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (SMulZeroClass.toSMul.{u1, u3} S B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribSMul.toSMulZeroClass.{u1, u3} S B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))))) (DistribMulAction.toDistribSMul.{u1, u3} S B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u2, u1, u2, u3} (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) S (RingQuot.{u2} A _inst_3 s) B (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6)))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (Module.toDistribMulAction.{u1, u3} S B (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_6))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (Algebra.toModule.{u1, u3} S B _inst_2 _inst_6 _inst_7) (AlgHomClass.linearMapClass.{u1, u2, u3, max u3 u2} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7 (AlgHom.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7) (AlgHom.algHomClass.{u1, u2, u3} S (RingQuot.{u2} A _inst_3 s) B _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_6 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) _inst_7))))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => RingQuot.{u2} A _inst_3 s) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (SMulZeroClass.toSMul.{u1, u2} S A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} S A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} S A (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4))))) (SMulZeroClass.toSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toZero.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribSMul.toSMulZeroClass.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (AddMonoid.toAddZeroClass.{u2} (RingQuot.{u2} A _inst_3 s) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))))) (DistribMulAction.toDistribSMul.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) S A (RingQuot.{u2} A _inst_3 s) (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S _inst_2))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddCommMonoid.toAddMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s))))) (Module.toDistribMulAction.{u1, u2} S A (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4)) (Module.toDistribMulAction.{u1, u2} S (RingQuot.{u2} A _inst_3 s) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (CommSemiring.toSemiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (RingQuot.{u2} A _inst_3 s) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (Semiring.toNonAssocSemiring.{u2} (RingQuot.{u2} A _inst_3 s) (RingQuot.instSemiring.{u2} A _inst_3 s)))) (Algebra.toModule.{u1, u2} S A _inst_2 _inst_3 _inst_4) (Algebra.toModule.{u1, u2} S (RingQuot.{u2} A _inst_3 s) _inst_2 (RingQuot.instSemiring.{u2} A _inst_3 s) (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHomClass.linearMapClass.{u1, u2, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s) (AlgHom.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)) (AlgHom.algHomClass.{u1, u2, u2} S A (RingQuot.{u2} A _inst_3 s) _inst_2 _inst_3 (RingQuot.instSemiring.{u2} A _inst_3 s) _inst_4 (RingQuot.instAlgebraRingQuotInstSemiring.{u2, u1} A _inst_3 S _inst_2 _inst_4 s)))))) (RingQuot.mkAlgHom.{u1, u2} S _inst_2 A _inst_3 _inst_4 s) y)))))))
+Case conversion may be inaccurate. Consider using '#align ring_quot.eq_lift_alg_hom_comp_mk_alg_hom RingQuot.eq_liftAlgHom_comp_mkAlgHomₓ'. -/
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
     f =
       liftAlgHom S

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebra.ring_quot
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit e5820f6c8fcf1b75bcd7738ae4da1c5896191f72
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -35,6 +35,23 @@ variable {S : Type u₂} [CommSemiring S]
 
 variable {A : Type u₃} [Semiring A] [Algebra S A]
 
+namespace RingCon
+
+instance (c : RingCon A) : Algebra S c.Quotient
+    where
+  smul := (· • ·)
+  toRingHom := c.mk'.comp (algebraMap S A)
+  commutes' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.commutes _ _
+  smul_def' r := Quotient.ind' fun a => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
+
+@[simp, norm_cast]
+theorem coe_algebraMap (c : RingCon A) (s : S) :
+    (↑(algebraMap S A s) : c.Quotient) = algebraMap S _ s :=
+  rfl
+#align ring_con.coe_algebra_map RingCon.coe_algebraMap
+
+end RingCon
+
 namespace RingQuot
 
 /-- Given an arbitrary relation `r` on a ring, we strengthen it to a relation `rel r`,
@@ -70,6 +87,69 @@ theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) :
   simp only [Algebra.smul_def, rel.mul_right h]
 #align ring_quot.rel.smul RingQuot.Rel.smul
 
+/-- `eqv_gen (ring_quot.rel r)` is a ring congruence. -/
+def ringCon (r : R → R → Prop) : RingCon R
+    where
+  R := EqvGen (Rel r)
+  iseqv := EqvGen.is_equivalence _
+  add' a b c d hab hcd :=
+    by
+    induction' hab with a' b' hab e a' b' hab' _ c' d' e hcd' hde' ihcd' ihde' generalizing c d
+    · refine' (EqvGen.rel _ _ hab.add_left).trans _ _ _ _
+      induction' hcd with c' d' hcd f c' d' hcd' habcd' c' d' f' hcd' hdf' hbcd' hbcf'
+      · exact EqvGen.rel _ _ hcd.add_right
+      · exact EqvGen.refl _
+      · exact habcd'.symm _ _
+      · exact hbcd'.trans _ _ _ hbcf'
+    · induction' hcd with c' d' hcd f c' d' hcd' habcd' c' d' f' hcd' hdf' hbcd' hbcf'
+      · exact EqvGen.rel _ _ hcd.add_right
+      · exact EqvGen.refl _
+      · exact EqvGen.symm _ _ habcd'
+      · exact hbcd'.trans _ _ _ hbcf'
+    · exact (hab_ih _ _ <| hcd.symm _ _).symm _ _
+    · exact (ihcd' _ _ hcd).trans _ _ _ (ihde' _ _ <| EqvGen.refl _)
+  mul' a b c d hab hcd :=
+    by
+    induction' hab with a' b' hab e a' b' hab' _ c' d' e hcd' hde' ihcd' ihde' generalizing c d
+    · refine' (EqvGen.rel _ _ hab.mul_left).trans _ _ _ _
+      induction' hcd with c' d' hcd f c' d' hcd' habcd' c' d' f' hcd' hdf' hbcd' hbcf'
+      · exact EqvGen.rel _ _ hcd.mul_right
+      · exact EqvGen.refl _
+      · exact habcd'.symm _ _
+      · exact hbcd'.trans _ _ _ hbcf'
+    · induction' hcd with c' d' hcd f c' d' hcd' habcd' c' d' f' hcd' hdf' hbcd' hbcf'
+      · exact EqvGen.rel _ _ hcd.mul_right
+      · exact EqvGen.refl _
+      · exact EqvGen.symm _ _ habcd'
+      · exact hbcd'.trans _ _ _ hbcf'
+    · exact (hab_ih _ _ <| hcd.symm _ _).symm _ _
+    · exact (ihcd' _ _ hcd).trans _ _ _ (ihde' _ _ <| EqvGen.refl _)
+#align ring_quot.ring_con RingQuot.ringCon
+
+theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r :=
+  by
+  ext (x₁ x₂)
+  constructor
+  · intro h
+    induction' h with x₃ x₄ h₃₄
+    · induction' h₃₄ with _ dfg h₃₄ x₃ x₄ x₅ h₃₄'
+      · exact RingConGen.Rel.of _ _ ‹_›
+      · exact h₃₄_ih.add (RingConGen.Rel.refl _)
+      · exact h₃₄_ih.mul (RingConGen.Rel.refl _)
+      · exact (RingConGen.Rel.refl _).mul h₃₄_ih
+    · exact RingConGen.Rel.refl _
+    · exact RingConGen.Rel.symm ‹_›
+    · exact RingConGen.Rel.trans ‹_› ‹_›
+  · intro h
+    induction h
+    · exact EqvGen.rel _ _ (rel.of ‹_›)
+    · exact (RingQuot.ringCon r).refl _
+    · exact (RingQuot.ringCon r).symm ‹_›
+    · exact (RingQuot.ringCon r).trans ‹_› ‹_›
+    · exact (RingQuot.ringCon r).add ‹_› ‹_›
+    · exact (RingQuot.ringCon r).mul ‹_› ‹_›
+#align ring_quot.eqv_gen_rel_eq RingQuot.eqvGen_rel_eq
+
 end RingQuot
 
 /-- The quotient of a ring by an arbitrary relation. -/

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

This renames

• Int.cast_ofNat to Int.cast_natCast
• Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

@@ -374,7 +374,7 @@ instance instRing {R : Type uR} [Ring R] (r : R → R → Prop) : Ring (RingQuot
       simp [smul_quot, neg_quot, add_mul]
     intCast := intCast r
     intCast_ofNat := fun n => congrArg RingQuot.mk <| by
-      exact congrArg (Quot.mk _) (Int.cast_ofNat _)
+      exact congrArg (Quot.mk _) (Int.cast_natCast _)
     intCast_negSucc := fun n => congrArg RingQuot.mk <| by
       simp_rw [neg_def]
       exact congrArg (Quot.mk _) (Int.cast_negSucc n) }

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -188,7 +188,7 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
             -- Porting note:
             -- `simpa [mul_def] using congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih`
             -- mysteriously doesn't work
-            have := congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih
+            have := congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) ih (Quot.sound h)
             dsimp only at this
             simp? [mul_def] at this says simp only [mul_def, Quot.map₂_mk, mk.injEq] at this
             exact this)

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)

@@ -26,10 +26,8 @@ Since everything runs in parallel for quotients of `R`-algebras, we do that case
 universe uR uS uT uA u₄
 
 variable {R : Type uR} [Semiring R]
-
 variable {S : Type uS} [CommSemiring S]
 variable {T : Type uT}
-
 variable {A : Type uA} [Semiring A] [Algebra S A]
 
 namespace RingCon

... or reduce its scope (the full removal is not as obvious).

@@ -23,10 +23,7 @@ definition, which is made irreducible for this purpose.
 Since everything runs in parallel for quotients of `R`-algebras, we do that case at the same time.
 -/
 
-set_option autoImplicit true
-
-
-universe uR uS uT uA
+universe uR uS uT uA u₄
 
 variable {R : Type uR} [Semiring R]
 

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

This follows on from #6964.

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

@@ -629,8 +629,8 @@ theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) :
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
 
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
-  suffices : Function.Surjective fun x ↦ (⟨.mk (Rel s) x⟩ : RingQuot s)
-  · simpa [mkAlgHom_def, mkRingHom_def]
+  suffices Function.Surjective fun x ↦ (⟨.mk (Rel s) x⟩ : RingQuot s) by
+    simpa [mkAlgHom_def, mkRingHom_def]
   rintro ⟨⟨a⟩⟩
   use a
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective

Subset of #9319

@@ -278,11 +278,11 @@ theorem smul_quot [Algebra S R] {n : S} {a : R} :
 
 instance instIsScalarTower [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R]
     [IsScalarTower S T R] : IsScalarTower S T (RingQuot r) :=
-  ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_assoc]⟩
+  ⟨fun s t ⟨a⟩ => Quot.inductionOn a fun a' => by simp only [RingQuot.smul_quot, smul_assoc]⟩
 
 instance instSMulCommClass [CommSemiring T] [Algebra S R] [Algebra T R] [SMulCommClass S T R] :
     SMulCommClass S T (RingQuot r) :=
-  ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_comm]⟩
+  ⟨fun s t ⟨a⟩ => Quot.inductionOn a fun a' => by simp only [RingQuot.smul_quot, smul_comm]⟩
 
 instance instAddCommMonoid (r : R → R → Prop) : AddCommMonoid (RingQuot r) where
   add := (· + ·)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -195,7 +195,7 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
             -- mysteriously doesn't work
             have := congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih
             dsimp only at this
-            simp [mul_def] at this
+            simp? [mul_def] at this says simp only [mul_def, Quot.map₂_mk, mk.injEq] at this
             exact this)
         a⟩
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -218,7 +218,7 @@ instance : Add (RingQuot r) :=
 instance : Mul (RingQuot r) :=
   ⟨mul r⟩
 
-instance : Pow (RingQuot r) ℕ :=
+instance : NatPow (RingQuot r) :=
   ⟨fun x n ↦ npow r n x⟩
 
 instance {R : Type uR} [Ring R] (r : R → R → Prop) : Neg (RingQuot r) :=

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

@@ -623,8 +623,9 @@ theorem mkAlgHom_coe (s : A → A → Prop) : (mkAlgHom S s : A →+* RingQuot s
   rfl
 #align ring_quot.mk_alg_hom_coe RingQuot.mkAlgHom_coe
 
-theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s x = mkAlgHom S s y :=
-  by simp [mkAlgHom_def, mkRingHom_def, Quot.sound (Rel.of w)]
+theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) :
+    mkAlgHom S s x = mkAlgHom S s y := by
+  simp [mkAlgHom_def, mkRingHom_def, Quot.sound (Rel.of w)]
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
 
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by

Removes nonterminal simps on lines looking like simp [...]

@@ -426,7 +426,7 @@ theorem mkRingHom_rel {r : R → R → Prop} {x y : R} (w : r x y) : mkRingHom r
 #align ring_quot.mk_ring_hom_rel RingQuot.mkRingHom_rel
 
 theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRingHom r) := by
-  simp [mkRingHom_def]
+  simp only [mkRingHom_def, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk]
   rintro ⟨⟨⟩⟩
   simp
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective

@@ -276,13 +276,11 @@ theorem smul_quot [Algebra S R] {n : S} {a : R} :
   rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
 
-instance instIsScalarTowerRingQuot [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R]
-    [IsScalarTower S T R] :
-    IsScalarTower S T (RingQuot r) :=
+instance instIsScalarTower [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R]
+    [IsScalarTower S T R] : IsScalarTower S T (RingQuot r) :=
   ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_assoc]⟩
 
-instance instSMulCommClassRingQuot [CommSemiring T] [Algebra S R] [Algebra T R]
-    [SMulCommClass S T R] :
+instance instSMulCommClass [CommSemiring T] [Algebra S R] [Algebra T R] [SMulCommClass S T R] :
     SMulCommClass S T (RingQuot r) :=
   ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_comm]⟩
 
@@ -396,10 +394,10 @@ instance instCommSemiring {R : Type uR} [CommSemiring R] (r : R → R → Prop)
 instance {R : Type uR} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
   { RingQuot.instCommSemiring r, RingQuot.instRing r with }
 
-instance instInhabitedRingQuot (r : R → R → Prop) : Inhabited (RingQuot r) :=
+instance instInhabited (r : R → R → Prop) : Inhabited (RingQuot r) :=
   ⟨0⟩
 
-instance instAlgebraRingQuot [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r) where
+instance instAlgebra [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r) where
   smul := (· • ·)
   toFun r := ⟨Quot.mk _ (algebraMap S R r)⟩
   map_one' := by simp [← one_quot]

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -23,6 +23,8 @@ definition, which is made irreducible for this purpose.
 Since everything runs in parallel for quotients of `R`-algebras, we do that case at the same time.
 -/
 
+set_option autoImplicit true
+
 
 universe uR uS uT uA
 

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -274,11 +274,13 @@ theorem smul_quot [Algebra S R] {n : S} {a : R} :
   rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
 
-instance [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R] [IsScalarTower S T R] :
+instance instIsScalarTowerRingQuot [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R]
+    [IsScalarTower S T R] :
     IsScalarTower S T (RingQuot r) :=
   ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_assoc]⟩
 
-instance [CommSemiring T] [Algebra S R] [Algebra T R] [SMulCommClass S T R] :
+instance instSMulCommClassRingQuot [CommSemiring T] [Algebra S R] [Algebra T R]
+    [SMulCommClass S T R] :
     SMulCommClass S T (RingQuot r) :=
   ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_comm]⟩
 
@@ -392,10 +394,10 @@ instance instCommSemiring {R : Type uR} [CommSemiring R] (r : R → R → Prop)
 instance {R : Type uR} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
   { RingQuot.instCommSemiring r, RingQuot.instRing r with }
 
-instance (r : R → R → Prop) : Inhabited (RingQuot r) :=
+instance instInhabitedRingQuot (r : R → R → Prop) : Inhabited (RingQuot r) :=
   ⟨0⟩
 
-instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r) where
+instance instAlgebraRingQuot [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r) where
   smul := (· • ·)
   toFun r := ⟨Quot.mk _ (algebraMap S R r)⟩
   map_one' := by simp [← one_quot]

This is pre-work towards a base-change of clifford algebras.

The main result here is

@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
    [Algebra R A] [Module R M] [Module A M]
    [IsScalarTower R A M] :
    Algebra R (TensorAlgebra A M)

Note that strictly the IsScalarTower R A M argument isn't needed, but I'd claim the instance doesn't make any sense without it.

In order to prevent diamonds in the algebraMap fields of the Int and Nat algebra instances, we have stop having natCast as an irreducible_def, and we have to add a missing intCast customization for RingQuot. In order to prevent diamonds in the smul fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the smul definition as an irreducible_def. We already had to make a similar refactor to prevent diamonds for Algebra R (Polynomial A).

If we backport any of this to mathlib3, we'd additionally have to change the smul definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.

These diamonds are tested with inline examples.

@@ -155,7 +155,8 @@ namespace RingQuot
 
 variable (r : R → R → Prop)
 
-private irreducible_def natCast (n : ℕ) : RingQuot r :=
+-- can't be irreducible, causes diamonds in ℕ-algebras
+private def natCast (n : ℕ) : RingQuot r :=
   ⟨Quot.mk _ n⟩
 
 private irreducible_def zero : RingQuot r :=
@@ -196,9 +197,13 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
             exact this)
         a⟩
 
-private irreducible_def smul [Algebra S R] (n : S) : RingQuot r → RingQuot r
+-- note: this cannot be irreducible, as otherwise diamonds don't commute.
+private def smul [Algebra S R] (n : S) : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (fun a ↦ n • a) (Rel.smul n) a⟩
 
+instance : NatCast (RingQuot r) :=
+  ⟨natCast r⟩
+
 instance : Zero (RingQuot r) :=
   ⟨zero r⟩
 
@@ -265,7 +270,7 @@ theorem sub_quot {R : Type uR} [Ring R] (r : R → R → Prop) {a b} :
 theorem smul_quot [Algebra S R] {n : S} {a : R} :
     (n • ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (n • a)⟩ := by
   show smul r _ _ = _
-  rw [smul_def]
+  rw [smul]
   rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
 
@@ -327,8 +332,8 @@ instance instMonoidWithZero (r : R → R → Prop) : MonoidWithZero (RingQuot r)
 
 instance instSemiring (r : R → R → Prop) : Semiring (RingQuot r) where
   natCast := natCast r
-  natCast_zero := by simp [Nat.cast, natCast_def, ← zero_quot]
-  natCast_succ := by simp [Nat.cast, natCast_def, ← one_quot, add_quot]
+  natCast_zero := by simp [Nat.cast, natCast, ← zero_quot]
+  natCast_succ := by simp [Nat.cast, natCast, ← one_quot, add_quot]
   left_distrib := by
     rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨⟨⟩⟩
     simp only [mul_quot, add_quot, left_distrib]
@@ -346,6 +351,10 @@ instance instSemiring (r : R → R → Prop) : Semiring (RingQuot r) where
   __ := instAddCommMonoid r
   __ := instMonoidWithZero r
 
+-- can't be irreducible, causes diamonds in ℤ-algebras
+private def intCast {R : Type uR} [Ring R] (r : R → R → Prop) (z : ℤ) : RingQuot r :=
+  ⟨Quot.mk _ z⟩
+
 instance instRing {R : Type uR} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
   { RingQuot.instSemiring r with
     neg := Neg.neg
@@ -365,7 +374,13 @@ instance instRing {R : Type uR} [Ring R] (r : R → R → Prop) : Ring (RingQuot
       simp [smul_quot, add_quot, add_mul, add_comm]
     zsmul_neg' := by
       rintro n ⟨⟨⟩⟩
-      simp [smul_quot, neg_quot, add_mul] }
+      simp [smul_quot, neg_quot, add_mul]
+    intCast := intCast r
+    intCast_ofNat := fun n => congrArg RingQuot.mk <| by
+      exact congrArg (Quot.mk _) (Int.cast_ofNat _)
+    intCast_negSucc := fun n => congrArg RingQuot.mk <| by
+      simp_rw [neg_def]
+      exact congrArg (Quot.mk _) (Int.cast_negSucc n) }
 
 instance instCommSemiring {R : Type uR} [CommSemiring R] (r : R → R → Prop) :
   CommSemiring (RingQuot r) :=

I tidied up some universe and type variables in the RingQuot file while I was here (in the first commit).

@@ -24,13 +24,14 @@ Since everything runs in parallel for quotients of `R`-algebras, we do that case
 -/
 
 
-universe u₁ u₂ u₃ u₄
+universe uR uS uT uA
 
-variable {R : Type u₁} [Semiring R]
+variable {R : Type uR} [Semiring R]
 
-variable {S : Type u₂} [CommSemiring S]
+variable {S : Type uS} [CommSemiring S]
+variable {T : Type uT}
 
-variable {A : Type u₃} [Semiring A] [Algebra S A]
+variable {A : Type uA} [Semiring A] [Algebra S A]
 
 namespace RingCon
 
@@ -66,15 +67,15 @@ theorem Rel.add_right {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) : R
   exact Rel.add_left h
 #align ring_quot.rel.add_right RingQuot.Rel.add_right
 
-theorem Rel.neg {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b : R⦄ (h : Rel r a b) :
+theorem Rel.neg {R : Type uR} [Ring R] {r : R → R → Prop} ⦃a b : R⦄ (h : Rel r a b) :
     Rel r (-a) (-b) := by simp only [neg_eq_neg_one_mul a, neg_eq_neg_one_mul b, Rel.mul_right h]
 #align ring_quot.rel.neg RingQuot.Rel.neg
 
-theorem Rel.sub_left {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r a b) :
+theorem Rel.sub_left {R : Type uR} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r a b) :
     Rel r (a - c) (b - c) := by simp only [sub_eq_add_neg, h.add_left]
 #align ring_quot.rel.sub_left RingQuot.Rel.sub_left
 
-theorem Rel.sub_right {R : Type u₁} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) :
+theorem Rel.sub_right {R : Type uR} [Ring R] {r : R → R → Prop} ⦃a b c : R⦄ (h : Rel r b c) :
     Rel r (a - b) (a - c) := by simp only [sub_eq_add_neg, h.neg.add_right]
 #align ring_quot.rel.sub_right RingQuot.Rel.sub_right
 
@@ -169,10 +170,10 @@ private irreducible_def add : RingQuot r → RingQuot r → RingQuot r
 private irreducible_def mul : RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ (· * ·) Rel.mul_right Rel.mul_left a b⟩
 
-private irreducible_def neg {R : Type u₁} [Ring R] (r : R → R → Prop) : RingQuot r → RingQuot r
+private irreducible_def neg {R : Type uR} [Ring R] (r : R → R → Prop) : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (fun a ↦ -a) Rel.neg a⟩
 
-private irreducible_def sub {R : Type u₁} [Ring R] (r : R → R → Prop) :
+private irreducible_def sub {R : Type uR} [Ring R] (r : R → R → Prop) :
   RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ Sub.sub Rel.sub_right Rel.sub_left a b⟩
 
@@ -213,10 +214,10 @@ instance : Mul (RingQuot r) :=
 instance : Pow (RingQuot r) ℕ :=
   ⟨fun x n ↦ npow r n x⟩
 
-instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Neg (RingQuot r) :=
+instance {R : Type uR} [Ring R] (r : R → R → Prop) : Neg (RingQuot r) :=
   ⟨neg r⟩
 
-instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Sub (RingQuot r) :=
+instance {R : Type uR} [Ring R] (r : R → R → Prop) : Sub (RingQuot r) :=
   ⟨sub r⟩
 
 instance [Algebra S R] : SMul S (RingQuot r) :=
@@ -247,14 +248,14 @@ theorem pow_quot {a} {n : ℕ} : (⟨Quot.mk _ a⟩ ^ n : RingQuot r) = ⟨Quot.
   rw [npow_def]
 #align ring_quot.pow_quot RingQuot.pow_quot
 
-theorem neg_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a} :
+theorem neg_quot {R : Type uR} [Ring R] (r : R → R → Prop) {a} :
     (-⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (-a)⟩ := by
   show neg r _ = _
   rw [neg_def]
   rfl
 #align ring_quot.neg_quot RingQuot.neg_quot
 
-theorem sub_quot {R : Type u₁} [Ring R] (r : R → R → Prop) {a b} :
+theorem sub_quot {R : Type uR} [Ring R] (r : R → R → Prop) {a b} :
     (⟨Quot.mk _ a⟩ - ⟨Quot.mk _ b⟩ : RingQuot r) = ⟨Quot.mk _ (a - b)⟩ := by
   show sub r _ _ = _
   rw [sub_def]
@@ -268,6 +269,14 @@ theorem smul_quot [Algebra S R] {n : S} {a : R} :
   rfl
 #align ring_quot.smul_quot RingQuot.smul_quot
 
+instance [CommSemiring T] [SMul S T] [Algebra S R] [Algebra T R] [IsScalarTower S T R] :
+    IsScalarTower S T (RingQuot r) :=
+  ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_assoc]⟩
+
+instance [CommSemiring T] [Algebra S R] [Algebra T R] [SMulCommClass S T R] :
+    SMulCommClass S T (RingQuot r) :=
+  ⟨fun s t ⟨a⟩ => Quot.inductionOn a <| fun a' => by simp only [RingQuot.smul_quot, smul_comm]⟩
+
 instance instAddCommMonoid (r : R → R → Prop) : AddCommMonoid (RingQuot r) where
   add := (· + ·)
   zero := 0
@@ -337,7 +346,7 @@ instance instSemiring (r : R → R → Prop) : Semiring (RingQuot r) where
   __ := instAddCommMonoid r
   __ := instMonoidWithZero r
 
-instance instRing {R : Type u₁} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
+instance instRing {R : Type uR} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
   { RingQuot.instSemiring r with
     neg := Neg.neg
     add_left_neg := by
@@ -358,14 +367,14 @@ instance instRing {R : Type u₁} [Ring R] (r : R → R → Prop) : Ring (RingQu
       rintro n ⟨⟨⟩⟩
       simp [smul_quot, neg_quot, add_mul] }
 
-instance instCommSemiring {R : Type u₁} [CommSemiring R] (r : R → R → Prop) :
+instance instCommSemiring {R : Type uR} [CommSemiring R] (r : R → R → Prop) :
   CommSemiring (RingQuot r) :=
   { RingQuot.instSemiring r with
     mul_comm := by
       rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
       simp [mul_quot, mul_comm] }
 
-instance {R : Type u₁} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
+instance {R : Type uR} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
   { RingQuot.instCommSemiring r, RingQuot.instRing r with }
 
 instance (r : R → R → Prop) : Inhabited (RingQuot r) :=
@@ -406,14 +415,14 @@ theorem mkRingHom_surjective (r : R → R → Prop) : Function.Surjective (mkRin
 #align ring_quot.mk_ring_hom_surjective RingQuot.mkRingHom_surjective
 
 @[ext 1100]
-theorem ringQuot_ext {T : Type u₄} [Semiring T] {r : R → R → Prop} (f g : RingQuot r →+* T)
+theorem ringQuot_ext [Semiring T] {r : R → R → Prop} (f g : RingQuot r →+* T)
     (w : f.comp (mkRingHom r) = g.comp (mkRingHom r)) : f = g := by
   ext x
   rcases mkRingHom_surjective r x with ⟨x, rfl⟩
   exact (RingHom.congr_fun w x : _)
 #align ring_quot.ring_quot_ext RingQuot.ringQuot_ext
 
-variable {T : Type u₄} [Semiring T]
+variable [Semiring T]
 
 irreducible_def preLift {r : R → R → Prop} { f : R →+* T } (h : ∀ ⦃x y⦄, r x y → f x = f y) :
   RingQuot r →+* T :=
@@ -482,7 +491,7 @@ agrees with the quotient by the appropriate ideal.
 -/
 
 
-variable {B : Type u₁} [CommRing B]
+variable {B : Type uR} [CommRing B]
 
 /-- The universal ring homomorphism from `RingQuot r` to `B ⧸ Ideal.ofRel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
@@ -564,7 +573,7 @@ theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
 #align ring_quot.star'_quot RingQuot.star'_quot
 
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/
-def starRing {R : Type u₁} [Semiring R] [StarRing R] (r : R → R → Prop)
+def starRing {R : Type uR} [Semiring R] [StarRing R] (r : R → R → Prop)
     (hr : ∀ a b, r a b → r (star a) (star b)) : StarRing (RingQuot r) where
   star := star' r hr
   star_involutive := by

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.ring_quot
-! leanprover-community/mathlib commit e5820f6c8fcf1b75bcd7738ae4da1c5896191f72
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Hom
 import Mathlib.RingTheory.Ideal.Quotient
 
+#align_import algebra.ring_quot from "leanprover-community/mathlib"@"e5820f6c8fcf1b75bcd7738ae4da1c5896191f72"
+
 /-!
 # Quotients of non-commutative rings
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -606,7 +606,7 @@ theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s
 
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
   suffices : Function.Surjective fun x ↦ (⟨.mk (Rel s) x⟩ : RingQuot s)
-  · simpa  [mkAlgHom_def, mkRingHom_def]
+  · simpa [mkAlgHom_def, mkRingHom_def]
   rintro ⟨⟨a⟩⟩
   use a
 #align ring_quot.mk_alg_hom_surjective RingQuot.mkAlgHom_surjective
@@ -645,7 +645,7 @@ irreducible_def preLiftAlgHom {s : A → A → Prop} { f : A →ₐ[S] B }
     simp [← one_quot, smul_quot, Algebra.algebraMap_eq_smul_one] }
 
 /-- Any `S`-algebra homomorphism `f : A →ₐ[S] B` which respects a relation `s : A → A → Prop`
-factors uniquely through a morphism `RingQuot s →ₐ[S]  B`.
+factors uniquely through a morphism `RingQuot s →ₐ[S] B`.
 -/
 irreducible_def liftAlgHom {s : A → A → Prop} :
   { f : A →ₐ[S] B // ∀ ⦃x y⦄, s x y → f x = f y } ≃ (RingQuot s →ₐ[S] B) :=

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -591,7 +591,7 @@ variable (S)
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
   { mkRingHom s with
-    commutes' := fun _ ↦ by simp [mkRingHom_def] ; rfl }
+    commutes' := fun _ ↦ by simp [mkRingHom_def]; rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
 @[simp]

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>

@@ -490,7 +490,7 @@ variable {B : Type u₁} [CommRing B]
 /-- The universal ring homomorphism from `RingQuot r` to `B ⧸ Ideal.ofRel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift ⟨Ideal.Quotient.mk (Ideal.ofRel r),
-        fun x y h ↦ Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr
+        fun x y h ↦ Ideal.Quotient.eq.2 <| Submodule.mem_sInf.mpr
           fun _ w ↦ w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 

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.)

@@ -564,7 +564,6 @@ private irreducible_def star' : RingQuot r → RingQuot r
 
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
     (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := star'_def _ _ _
-
 #align ring_quot.star'_quot RingQuot.star'_quot
 
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/

@@ -183,7 +183,7 @@ private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
   | ⟨a⟩ =>
     ⟨Quot.lift (fun a ↦ Quot.mk (RingQuot.Rel r) (a ^ n))
         (fun a b (h : Rel r a b) ↦ by
-          -- note we can't define a `rel.pow` as `rel` isn't reflexive so `rel r 1 1` isn't true
+          -- note we can't define a `Rel.pow` as `Rel` isn't reflexive so `Rel r 1 1` isn't true
           dsimp only
           induction n with
           | zero => rw [pow_zero, pow_zero]
@@ -340,7 +340,7 @@ instance instSemiring (r : R → R → Prop) : Semiring (RingQuot r) where
   __ := instAddCommMonoid r
   __ := instMonoidWithZero r
 
-instance Ring {R : Type u₁} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
+instance instRing {R : Type u₁} [Ring R] (r : R → R → Prop) : Ring (RingQuot r) :=
   { RingQuot.instSemiring r with
     neg := Neg.neg
     add_left_neg := by
@@ -369,7 +369,7 @@ instance instCommSemiring {R : Type u₁} [CommSemiring R] (r : R → R → Prop
       simp [mul_quot, mul_comm] }
 
 instance {R : Type u₁} [CommRing R] (r : R → R → Prop) : CommRing (RingQuot r) :=
-  { RingQuot.instCommSemiring r, RingQuot.Ring r with }
+  { RingQuot.instCommSemiring r, RingQuot.instRing r with }
 
 instance (r : R → R → Prop) : Inhabited (RingQuot r) :=
   ⟨0⟩
@@ -487,7 +487,7 @@ agrees with the quotient by the appropriate ideal.
 
 variable {B : Type u₁} [CommRing B]
 
-/-- The universal ring homomorphism from `RingQuot r` to `B ⧸ ideal.of_rel r`. -/
+/-- The universal ring homomorphism from `RingQuot r` to `B ⧸ Ideal.ofRel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
   lift ⟨Ideal.Quotient.mk (Ideal.ofRel r),
         fun x y h ↦ Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr

Those changes were meant to be part of #3383 that got prematurely merged after some abusive relabeling.

@@ -14,7 +14,7 @@ import Mathlib.RingTheory.Ideal.Quotient
 /-!
 # Quotients of non-commutative rings
 
-Unfortunately, ideals have only been developed in the commutative case as `ideal`,
+Unfortunately, ideals have only been developed in the commutative case as `Ideal`,
 and it's not immediately clear how one should formalise ideals in the non-commutative case.
 
 In this file, we directly define the quotient of a semiring by any relation,
@@ -40,11 +40,12 @@ namespace RingCon
 instance (c : RingCon A) : Algebra S c.Quotient where
   smul := (· • ·)
   toRingHom := c.mk'.comp (algebraMap S A)
-  commutes' _ := Quotient.ind' fun _ => congr_arg Quotient.mk'' <| Algebra.commutes _ _
-  smul_def' _ := Quotient.ind' fun _ => congr_arg Quotient.mk'' <| Algebra.smul_def _ _
+  commutes' _ := Quotient.ind' fun _ ↦ congr_arg Quotient.mk'' <| Algebra.commutes _ _
+  smul_def' _ := Quotient.ind' fun _ ↦ congr_arg Quotient.mk'' <| Algebra.smul_def _ _
+
 @[simp, norm_cast]
 theorem coe_algebraMap (c : RingCon A) (s : S) :
-    (↑(algebraMap S A s) : c.Quotient) = algebraMap S _ s :=
+    (algebraMap S A s : c.Quotient) = algebraMap S _ s :=
   rfl
 #align ring_con.coe_algebra_map RingCon.coe_algebraMap
 
@@ -52,8 +53,8 @@ end RingCon
 
 namespace RingQuot
 
-/-- Given an arbitrary relation `r` on a ring, we strengthen it to a relation `rel r`,
-such that the equivalence relation generated by `rel r` has `x ~ y` if and only if
+/-- Given an arbitrary relation `r` on a ring, we strengthen it to a relation `Rel r`,
+such that the equivalence relation generated by `Rel r` has `x ~ y` if and only if
 `x - y` is in the ideal generated by elements `a - b` such that `r a b`.
 -/
 inductive Rel (r : R → R → Prop) : R → R → Prop
@@ -84,63 +85,65 @@ theorem Rel.smul {r : A → A → Prop} (k : S) ⦃a b : A⦄ (h : Rel r a b) :
   simp only [Algebra.smul_def, Rel.mul_right h]
 #align ring_quot.rel.smul RingQuot.Rel.smul
 
-/-- `eqv_gen (ring_quot.rel r)` is a ring congruence. -/
+/-- `EqvGen (RingQuot.Rel r)` is a ring congruence. -/
 def ringCon (r : R → R → Prop) : RingCon R where
   r := EqvGen (Rel r)
   iseqv := EqvGen.is_equivalence _
   add' {a b c d} hab hcd := by
-    induction' hab with a' b' hab e a' b' _ hab_ih c' d' e _ _ ihcd' ihde' generalizing c d
-    · refine' (EqvGen.rel _ _ hab.add_left).trans _ _ _ _
-      induction' hcd with c' d' hcd f c' d' _hcd' habcd' c' d' f' _hcd' _hdf' hbcd' hbcf'
-      · exact EqvGen.rel _ _ hcd.add_right
-      · exact EqvGen.refl _
-      · exact habcd'.symm _ _
-      · exact hbcd'.trans _ _ _ hbcf'
-    · induction' hcd with c' d' hcd f c' d' _hcd' habcd' c' d' f' _hcd' _hdf' hbcd' hbcf'
-      · exact EqvGen.rel _ _ hcd.add_right
-      · exact EqvGen.refl _
-      · exact EqvGen.symm _ _ habcd'
-      · exact hbcd'.trans _ _ _ hbcf'
-    · exact (hab_ih hcd.symm).symm
-    · exact (ihcd' hcd).trans _ _ _ (ihde' <| EqvGen.refl _)
+    induction hab generalizing c d with
+    | rel _ _ hab =>
+      refine' (EqvGen.rel _ _ hab.add_left).trans _ _ _ _
+      induction hcd with
+      | rel _ _ hcd => exact EqvGen.rel _ _ hcd.add_right
+      | refl => exact EqvGen.refl _
+      | symm _ _ _ h => exact h.symm _ _
+      | trans _ _ _ _ _ h h' => exact h.trans _ _ _ h'
+    | refl => induction hcd with
+      | rel _ _ hcd => exact EqvGen.rel _ _ hcd.add_right
+      | refl => exact EqvGen.refl _
+      | symm _ _ _ h => exact h.symm _ _
+      | trans _ _ _ _ _ h h' => exact h.trans _ _ _ h'
+    | symm x y _ hxy => exact (hxy hcd.symm).symm
+    | trans x y z _ _ h h' => exact (h hcd).trans _ _ _ (h' <| EqvGen.refl _)
   mul' {a b c d} hab hcd := by
-    induction' hab with a' b' hab e a' b' _ ihhab c' d' e _ _ ihcd' ihde' generalizing c d
-    · refine' (EqvGen.rel _ _ hab.mul_left).trans _ _ _ _
-      induction' hcd with c' d' hcd f c' d' _ habcd' c' d' f' _ _ hbcd' hbcf'
-      · exact EqvGen.rel _ _ hcd.mul_right
-      · exact EqvGen.refl _
-      · exact habcd'.symm _ _
-      · exact hbcd'.trans _ _ _ hbcf'
-    · induction' hcd with c' d' hcd f c' d' _ habcd' c' d' f' _ _ hbcd' hbcf'
-      · exact EqvGen.rel _ _ hcd.mul_right
-      · exact EqvGen.refl _
-      · exact EqvGen.symm _ _ habcd'
-      · exact hbcd'.trans _ _ _ hbcf'
-    · exact (ihhab <| hcd.symm _ _).symm _ _
-    · exact (ihcd' hcd).trans _ _ _ (ihde' <| EqvGen.refl _)
+    induction hab generalizing c d with
+    | rel _ _ hab =>
+      refine' (EqvGen.rel _ _ hab.mul_left).trans _ _ _ _
+      induction hcd with
+      | rel _ _ hcd => exact EqvGen.rel _ _ hcd.mul_right
+      | refl => exact EqvGen.refl _
+      | symm _ _ _ h => exact h.symm _ _
+      | trans _ _ _ _ _ h h' => exact h.trans _ _ _ h'
+    | refl => induction hcd with
+      | rel _ _ hcd => exact EqvGen.rel _ _ hcd.mul_right
+      | refl => exact EqvGen.refl _
+      | symm _ _ _ h => exact h.symm _ _
+      | trans _ _ _ _ _ h h' => exact h.trans _ _ _ h'
+    | symm x y _ hxy => exact (hxy hcd.symm).symm
+    | trans x y z _ _ h h' => exact (h hcd).trans _ _ _ (h' <| EqvGen.refl _)
 #align ring_quot.ring_con RingQuot.ringCon
 
 theorem eqvGen_rel_eq (r : R → R → Prop) : EqvGen (Rel r) = RingConGen.Rel r := by
-  ext (x₁ x₂)
+  ext x₁ x₂
   constructor
   · intro h
-    induction' h with x₃ x₄ h₃₄
-    · induction' h₃₄ with h₃₄_ih dfg h₃₄ x₃ x₄ x₅ _ h₃₄_ih _ _ _ _ h₃₄_ih _ _ _ _ h₃₄_ih
-      · exact RingConGen.Rel.of _ _ ‹_›
-      · exact h₃₄_ih.add (RingConGen.Rel.refl _)
-      · exact h₃₄_ih.mul (RingConGen.Rel.refl _)
-      · exact (RingConGen.Rel.refl _).mul h₃₄_ih
-    · exact RingConGen.Rel.refl _
-    · exact RingConGen.Rel.symm ‹_›
-    · exact RingConGen.Rel.trans ‹_› ‹_›
+    induction h with
+    | rel _ _ h => induction h with
+      | of => exact RingConGen.Rel.of _ _ ‹_›
+      | add_left _ h => exact h.add (RingConGen.Rel.refl _)
+      | mul_left _ h => exact h.mul (RingConGen.Rel.refl _)
+      | mul_right _ h => exact (RingConGen.Rel.refl _).mul h
+    | refl => exact RingConGen.Rel.refl _
+    | symm => exact RingConGen.Rel.symm ‹_›
+    | trans => exact RingConGen.Rel.trans ‹_› ‹_›
   · intro h
-    induction h
-    · exact EqvGen.rel _ _ (Rel.of ‹_›)
-    · exact (RingQuot.ringCon r).refl _
-    · exact (RingQuot.ringCon r).symm ‹_›
-    · exact (RingQuot.ringCon r).trans ‹_› ‹_›
-    · exact (RingQuot.ringCon r).add ‹_› ‹_›
-    · exact (RingQuot.ringCon r).mul ‹_› ‹_›
+    induction h with
+    | of => exact EqvGen.rel _ _ (Rel.of ‹_›)
+    | refl => exact (RingQuot.ringCon r).refl _
+    | symm => exact (RingQuot.ringCon r).symm ‹_›
+    | trans => exact (RingQuot.ringCon r).trans ‹_› ‹_›
+    | add => exact (RingQuot.ringCon r).add ‹_› ‹_›
+    | mul => exact (RingQuot.ringCon r).mul ‹_› ‹_›
 #align ring_quot.eqv_gen_rel_eq RingQuot.eqvGen_rel_eq
 
 end RingQuot
@@ -170,7 +173,7 @@ private irreducible_def mul : RingQuot r → RingQuot r → RingQuot r
   | ⟨a⟩, ⟨b⟩ => ⟨Quot.map₂ (· * ·) Rel.mul_right Rel.mul_left a b⟩
 
 private irreducible_def neg {R : Type u₁} [Ring R] (r : R → R → Prop) : RingQuot r → RingQuot r
-  | ⟨a⟩ => ⟨Quot.map (fun a => -a) Rel.neg a⟩
+  | ⟨a⟩ => ⟨Quot.map (fun a ↦ -a) Rel.neg a⟩
 
 private irreducible_def sub {R : Type u₁} [Ring R] (r : R → R → Prop) :
   RingQuot r → RingQuot r → RingQuot r
@@ -178,24 +181,25 @@ private irreducible_def sub {R : Type u₁} [Ring R] (r : R → R → Prop) :
 
 private irreducible_def npow (n : ℕ) : RingQuot r → RingQuot r
   | ⟨a⟩ =>
-    ⟨Quot.lift (fun a => Quot.mk (RingQuot.Rel r) (a ^ n))
-        (fun a b (h : Rel r a b) => by
+    ⟨Quot.lift (fun a ↦ Quot.mk (RingQuot.Rel r) (a ^ n))
+        (fun a b (h : Rel r a b) ↦ by
           -- note we can't define a `rel.pow` as `rel` isn't reflexive so `rel r 1 1` isn't true
           dsimp only
-          induction' n with n ih
-          · rw [pow_zero, pow_zero]
-          · rw [pow_succ, pow_succ]
+          induction n with
+          | zero => rw [pow_zero, pow_zero]
+          | succ n ih =>
+            rw [pow_succ, pow_succ]
             -- Porting note:
-            -- `simpa [mul_def] using congr_arg₂ (fun x y => mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih`
+            -- `simpa [mul_def] using congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih`
             -- mysteriously doesn't work
-            have := congr_arg₂ (fun x y => mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih
+            have := congr_arg₂ (fun x y ↦ mul r ⟨x⟩ ⟨y⟩) (Quot.sound h) ih
             dsimp only at this
             simp [mul_def] at this
             exact this)
         a⟩
 
 private irreducible_def smul [Algebra S R] (n : S) : RingQuot r → RingQuot r
-  | ⟨a⟩ => ⟨Quot.map (fun a => n • a) (Rel.smul n) a⟩
+  | ⟨a⟩ => ⟨Quot.map (fun a ↦ n • a) (Rel.smul n) a⟩
 
 instance : Zero (RingQuot r) :=
   ⟨zero r⟩
@@ -210,7 +214,7 @@ instance : Mul (RingQuot r) :=
   ⟨mul r⟩
 
 instance : Pow (RingQuot r) ℕ :=
-  ⟨fun x n => npow r n x⟩
+  ⟨fun x n ↦ npow r n x⟩
 
 instance {R : Type u₁} [Ring R] (r : R → R → Prop) : Neg (RingQuot r) :=
   ⟨neg r⟩
@@ -387,7 +391,7 @@ instance [Algebra S R] (r : R → R → Prop) : Algebra S (RingQuot r) where
 /-- The quotient map from a ring to its quotient, as a homomorphism of rings.
 -/
 irreducible_def mkRingHom (r : R → R → Prop) : R →+* RingQuot r :=
-  { toFun := fun x => ⟨Quot.mk _ x⟩
+  { toFun := fun x ↦ ⟨Quot.mk _ x⟩
     map_one' := by simp [← one_quot]
     map_mul' := by simp [mul_quot]
     map_zero' := by simp [← zero_quot]
@@ -416,15 +420,14 @@ variable {T : Type u₄} [Semiring T]
 
 irreducible_def preLift {r : R → R → Prop} { f : R →+* T } (h : ∀ ⦃x y⦄, r x y → f x = f y) :
   RingQuot r →+* T :=
-  { toFun := fun x =>
-      Quot.lift f
+  { toFun := fun x ↦ Quot.lift f
         (by
           rintro _ _ r
-          induction r
-          case of _ _ r => exact h r
-          case add_left _ _ _ _ r' => rw [map_add, map_add, r']
-          case mul_left _ _ _ _ r' => rw [map_mul, map_mul, r']
-          case mul_right _ _ _ _ r' => rw [map_mul, map_mul, r'])
+          induction r with
+          | of r => exact h r
+          | add_left _ r' => rw [map_add, map_add, r']
+          | mul_left _ r' => rw [map_mul, map_mul, r']
+          | mul_right _ r' => rw [map_mul, map_mul, r'])
         x.toQuot
     map_zero' := by simp only [← zero_quot, f.map_zero]
     map_add' := by
@@ -436,20 +439,17 @@ irreducible_def preLift {r : R → R → Prop} { f : R →+* T } (h : ∀ ⦃x y
       simp only [mul_quot, f.map_mul x y] }
 
 /-- Any ring homomorphism `f : R →+* T` which respects a relation `r : R → R → Prop`
-factors uniquely through a morphism `ring_quot r →+* T`.
+factors uniquely through a morphism `RingQuot r →+* T`.
 -/
 irreducible_def lift {r : R → R → Prop} :
   { f : R →+* T // ∀ ⦃x y⦄, r x y → f x = f y } ≃ (RingQuot r →+* T) :=
-  { toFun := fun f' => preLift f'.prop
-    invFun := fun F =>
-      ⟨F.comp (mkRingHom r), fun x y h => by
-        dsimp
-        rw [mkRingHom_rel h]⟩
-    left_inv := fun f => by
+  { toFun := fun f ↦ preLift f.prop
+    invFun := fun F ↦ ⟨F.comp (mkRingHom r), fun x y h ↦ congr_arg F (mkRingHom_rel h)⟩
+    left_inv := fun f ↦ by
       ext
       simp only [preLift_def, mkRingHom_def, RingHom.coe_comp, RingHom.coe_mk, MonoidHom.coe_mk,
                  OneHom.coe_mk, Function.comp_apply]
-    right_inv := fun F => by
+    right_inv := fun F ↦ by
       simp only [preLift_def]
       ext
       simp only [mkRingHom_def, RingHom.coe_comp, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk,
@@ -471,11 +471,7 @@ theorem lift_unique (f : R →+* T) {r : R → R → Prop} (w : ∀ ⦃x y⦄, r
 #align ring_quot.lift_unique RingQuot.lift_unique
 
 theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
-    f =
-      lift
-        ⟨f.comp (mkRingHom r), fun x y h => by
-          dsimp
-          rw [mkRingHom_rel h]⟩ := by
+    f = lift ⟨f.comp (mkRingHom r), fun x y h ↦ congr_arg f (mkRingHom_rel h)⟩ := by
   conv_lhs => rw [← lift.apply_symm_apply f]
   rw [lift_def]
   rfl
@@ -484,18 +480,18 @@ theorem eq_lift_comp_mkRingHom {r : R → R → Prop} (f : RingQuot r →+* T) :
 section CommRing
 
 /-!
-We now verify that in the case of a commutative ring, the `ring_quot` construction
+We now verify that in the case of a commutative ring, the `RingQuot` construction
 agrees with the quotient by the appropriate ideal.
 -/
 
 
 variable {B : Type u₁} [CommRing B]
 
-/-- The universal ring homomorphism from `ring_quot r` to `B ⧸ ideal.of_rel r`. -/
+/-- The universal ring homomorphism from `RingQuot r` to `B ⧸ ideal.of_rel r`. -/
 def ringQuotToIdealQuotient (r : B → B → Prop) : RingQuot r →+* B ⧸ Ideal.ofRel r :=
-  lift
-    ⟨Ideal.Quotient.mk (Ideal.ofRel r), fun x y h =>
-      Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr fun _ w => w ⟨x, y, h, sub_add_cancel x y⟩⟩
+  lift ⟨Ideal.Quotient.mk (Ideal.ofRel r),
+        fun x y h ↦ Ideal.Quotient.eq.2 <| Submodule.mem_infₛ.mpr
+          fun _ w ↦ w ⟨x, y, h, sub_add_cancel x y⟩⟩
 #align ring_quot.ring_quot_to_ideal_quotient RingQuot.ringQuotToIdealQuotient
 
 @[simp]
@@ -505,11 +501,11 @@ theorem ringQuotToIdealQuotient_apply (r : B → B → Prop) (x : B) :
   rfl
 #align ring_quot.ring_quot_to_ideal_quotient_apply RingQuot.ringQuotToIdealQuotient_apply
 
-/-- The universal ring homomorphism from `B ⧸ ideal.of_rel r` to `ring_quot r`. -/
+/-- The universal ring homomorphism from `B ⧸ Ideal.ofRel r` to `RingQuot r`. -/
 def idealQuotientToRingQuot (r : B → B → Prop) : B ⧸ Ideal.ofRel r →+* RingQuot r :=
   Ideal.Quotient.lift (Ideal.ofRel r) (mkRingHom r)
     (by
-      refine' fun x h => Submodule.span_induction h _ _ _ _
+      refine' fun x h ↦ Submodule.span_induction h _ _ _ _
       · rintro y ⟨a, b, h, su⟩
         symm at su
         rw [← sub_eq_iff_eq_add] at su
@@ -528,7 +524,7 @@ theorem idealQuotientToRingQuot_apply (r : B → B → Prop) (x : B) :
 #align ring_quot.ideal_quotient_to_ring_quot_apply RingQuot.idealQuotientToRingQuot_apply
 
 
-/-- The ring equivalence between `ring_quot r` and `(ideal.of_rel r).quotient`
+/-- The ring equivalence between `RingQuot r` and `(Ideal.ofRel r).quotient`
 -/
 def ringQuotEquivIdealQuotient (r : B → B → Prop) : RingQuot r ≃+* B ⧸ Ideal.ofRel r :=
   RingEquiv.ofHomInv (ringQuotToIdealQuotient r) (idealQuotientToRingQuot r)
@@ -554,23 +550,21 @@ variable [StarRing R] (hr : ∀ a b, r a b → r (star a) (star b))
 
 theorem Rel.star ⦃a b : R⦄ (h : Rel r a b) : Rel r (star a) (star b) := by
   induction h with
-  | of h                 => exact Rel.of (hr _ _ h)
-  | @add_left _ _ _ _ h  => rw [star_add, star_add]
-                            exact Rel.add_left h
-  | @mul_left _ _ _ _ h  => rw [star_mul, star_mul]
-                            exact Rel.mul_right h
-  | @mul_right _ _ _ _ h => rw [star_mul, star_mul]
-                            exact Rel.mul_left h
+  | of h          => exact Rel.of (hr _ _ h)
+  | add_left _ h  => rw [star_add, star_add]
+                     exact Rel.add_left h
+  | mul_left _ h  => rw [star_mul, star_mul]
+                     exact Rel.mul_right h
+  | mul_right _ h => rw [star_mul, star_mul]
+                     exact Rel.mul_left h
 #align ring_quot.rel.star RingQuot.Rel.star
 
 private irreducible_def star' : RingQuot r → RingQuot r
   | ⟨a⟩ => ⟨Quot.map (star : R → R) (Rel.star r hr) a⟩
 
 theorem star'_quot (hr : ∀ a b, r a b → r (star a) (star b)) {a} :
-    (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := by
-  show star' r _ _ = _
-  rw [star'_def]
-  rfl
+    (star' r hr ⟨Quot.mk _ a⟩ : RingQuot r) = ⟨Quot.mk _ (star a)⟩ := star'_def _ _ _
+
 #align ring_quot.star'_quot RingQuot.star'_quot
 
 /-- Transfer a star_ring instance through a quotient, if the quotient is invariant to `star` -/
@@ -598,9 +592,7 @@ variable (S)
 -/
 irreducible_def mkAlgHom (s : A → A → Prop) : A →ₐ[S] RingQuot s :=
   { mkRingHom s with
-    commutes' := fun r => by
-      simp [mkRingHom_def]
-      rfl }
+    commutes' := fun _ ↦ by simp [mkRingHom_def] ; rfl }
 #align ring_quot.mk_alg_hom RingQuot.mkAlgHom
 
 @[simp]
@@ -614,7 +606,7 @@ theorem mkAlgHom_rel {s : A → A → Prop} {x y : A} (w : s x y) : mkAlgHom S s
 #align ring_quot.mk_alg_hom_rel RingQuot.mkAlgHom_rel
 
 theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) := by
-  suffices : Function.Surjective fun x => (⟨.mk (Rel s) x⟩ : RingQuot s)
+  suffices : Function.Surjective fun x ↦ (⟨.mk (Rel s) x⟩ : RingQuot s)
   · simpa  [mkAlgHom_def, mkRingHom_def]
   rintro ⟨⟨a⟩⟩
   use a
@@ -632,15 +624,14 @@ theorem ringQuot_ext' {s : A → A → Prop} (f g : RingQuot s →ₐ[S] B)
 
 irreducible_def preLiftAlgHom {s : A → A → Prop} { f : A →ₐ[S] B }
   (h : ∀ ⦃x y⦄, s x y → f x = f y) : RingQuot s →ₐ[S] B :=
-{ toFun := fun x =>
-          Quot.lift f
+{ toFun := fun x ↦ Quot.lift f
             (by
               rintro _ _ r
-              induction r
-              case of _ _ r => exact h r
-              case add_left _ _ _ _ r' => simp only [map_add, r']
-              case mul_left _ _ _ _ r' => simp only [map_mul, r']
-              case mul_right _ _ _ _ r' => simp only [map_mul, r'])
+              induction r with
+              | of r => exact h r
+              | add_left _ r' => simp only [map_add, r']
+              | mul_left _ r' => simp only [map_mul, r']
+              | mul_right _ r' => simp only [map_mul, r'])
             x.toQuot
   map_zero' := by simp only [← zero_quot, f.map_zero]
   map_add' := by
@@ -655,21 +646,18 @@ irreducible_def preLiftAlgHom {s : A → A → Prop} { f : A →ₐ[S] B }
     simp [← one_quot, smul_quot, Algebra.algebraMap_eq_smul_one] }
 
 /-- Any `S`-algebra homomorphism `f : A →ₐ[S] B` which respects a relation `s : A → A → Prop`
-factors uniquely through a morphism `ring_quot s →ₐ[S]  B`.
+factors uniquely through a morphism `RingQuot s →ₐ[S]  B`.
 -/
 irreducible_def liftAlgHom {s : A → A → Prop} :
   { f : A →ₐ[S] B // ∀ ⦃x y⦄, s x y → f x = f y } ≃ (RingQuot s →ₐ[S] B) :=
-  { toFun := fun f' => preLiftAlgHom _ f'.prop
-    invFun := fun F =>
-      ⟨F.comp (mkAlgHom S s), fun _ _ h => by
-        dsimp
-        erw [mkAlgHom_rel S h]⟩
-    left_inv := fun f => by
+  { toFun := fun f' ↦ preLiftAlgHom _ f'.prop
+    invFun := fun F ↦ ⟨F.comp (mkAlgHom S s), fun _ _ h ↦ congr_arg F (mkAlgHom_rel S h)⟩
+    left_inv := fun f ↦ by
       ext
       simp only [preLiftAlgHom_def, mkAlgHom_def, mkRingHom_def, RingHom.toMonoidHom_eq_coe,
                  RingHom.coe_monoidHom_mk, AlgHom.coe_comp, AlgHom.coe_mk, RingHom.coe_mk,
                  MonoidHom.coe_mk, OneHom.coe_mk, Function.comp_apply]
-    right_inv := fun F => by
+    right_inv := fun F ↦ by
       ext
       simp only [preLiftAlgHom_def, mkAlgHom_def, mkRingHom_def, RingHom.toMonoidHom_eq_coe,
                  RingHom.coe_monoidHom_mk, AlgHom.coe_comp, AlgHom.coe_mk, RingHom.coe_mk,
@@ -683,7 +671,7 @@ theorem liftAlgHom_mkAlgHom_apply (f : A →ₐ[S] B) {s : A → A → Prop}
   rfl
 #align ring_quot.lift_alg_hom_mk_alg_hom_apply RingQuot.liftAlgHom_mkAlgHom_apply
 
--- note this is essentially `(lift_alg_hom S).symm_apply_eq.mp h`
+-- note this is essentially `(liftAlgHom S).symm_apply_eq.mp h`
 theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ ⦃x y⦄, s x y → f x = f y)
     (g : RingQuot s →ₐ[S] B) (h : g.comp (mkAlgHom S s) = f) : g = liftAlgHom S ⟨f, w⟩ := by
   ext
@@ -691,11 +679,7 @@ theorem liftAlgHom_unique (f : A →ₐ[S] B) {s : A → A → Prop} (w : ∀ 
 #align ring_quot.lift_alg_hom_unique RingQuot.liftAlgHom_unique
 
 theorem eq_liftAlgHom_comp_mkAlgHom {s : A → A → Prop} (f : RingQuot s →ₐ[S] B) :
-    f =
-      liftAlgHom S
-        ⟨f.comp (mkAlgHom S s), fun x y h => by
-          dsimp
-          erw [mkAlgHom_rel S h]⟩ := by
+    f = liftAlgHom S ⟨f.comp (mkAlgHom S s), fun x y h ↦ congr_arg f (mkAlgHom_rel S h)⟩ := by
   conv_lhs => rw [← (liftAlgHom S).apply_symm_apply f]
   rw [liftAlgHom]
   rfl