∀ {R : Type u_1} {S : Type u_2} (f : S → R),
  Function.Injective f →
    ∀ [inst : Add S] [inst_1 : Mul S] [inst_2 : Mul R] [inst_3 : Add R] [RightDistribClass R],
      (∀ (x y : S), f (x + y) = f x + f y) → (∀ (x y : S), f (x * y) = f x * f y) → RightDistribClass S