∀ (R : Type u_2) {S : Type u_3} (M : Type u_1) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : Group S] [inst_4 : DistribMulAction S M] [inst_5 : SMulCommClass S R M] (s : S) (m : R) (x : M),
  (DistribSMul.toLinearMap R M s).toFun (m • x) = (RingHom.id R) m • (DistribSMul.toLinearMap R M s).toFun x