∀ (α : Type u_1) (x : CommRing α) (M : Type u_2) (x_1 : AddCommGroup M) (x_2 : Module α M) (r : α) (rs : List α),
  RingTheory.Sequence.IsWeaklyRegular M (r :: rs) →
    IsSMulRegular M r ∧
      RingTheory.Sequence.IsWeaklyRegular (QuotSMulTop r M) (List.map (⇑(Ideal.Quotient.mk (Ideal.span {r}))) rs)