∀ {A : Type u_2} [inst : Ring A] {R : Type u_1} [inst_1 : CommRing R] [inst_2 : Algebra R A] {p : Ideal R} {P : Ideal A}
  [inst_3 : P.IsTwoSided] (h : p ≤ Ideal.comap (algebraMap R A) P) (r : R ⧸ p) (x : A ⧸ P),
  r • x = (Ideal.quotientMap P (algebraMap R A) h) r * x