∀ (S : Type u_3) [inst : CommSemiring S] {A : Type u_1} [inst_1 : Semiring A] [inst_2 : Algebra S A] {B : Type u_2}
  [inst_3 : Semiring B] [inst_4 : Algebra S B] {s : A → A → Prop} {f : A →ₐ[S] B} (h : ∀ ⦃x y : A⦄, s x y → f x = f y)
  (x y : RingQuot s), Quot.lift ⇑f ⋯ (x * y).toQuot = Quot.lift ⇑f ⋯ x.toQuot * Quot.lift ⇑f ⋯ y.toQuot