∀ {R : Type u_1} (S : Type u_2) (M : Type u_3) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : Module S M] [IsScalarTower R S M] (rs : List R),
  RingTheory.Sequence.IsWeaklyRegular M (List.map (⇑(algebraMap R S)) rs) ↔ RingTheory.Sequence.IsWeaklyRegular M rs