∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  (x : R) (x_1 : AdicCompletion.AdicCauchySequence I M),
  { toFun := Subtype.val, map_zero' := ⋯, map_add' := ⋯ } (x • x_1) =
    { toFun := Subtype.val, map_zero' := ⋯, map_add' := ⋯ } (x • x_1)