∀ (S : Type u_3) [inst : CommSemiring S] {A : Type u_2} [inst_1 : Semiring A] [inst_2 : Algebra S A] {B : Type u_1}
  [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)
  (r : S), Quot.lift ⇑f ⋯ ((algebraMap S (RingQuot s)) r).toQuot = (algebraMap S B) r