∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : AddCommGroup M] [inst_3 : AddCommGroup M₂] [inst_4 : Module R M] [inst_5 : Module S M₂] {e : M ≃+ M₂}
  {as : List R} {bs : List S},
  List.Forall₂ (fun r s => ∀ (x : M), e (r • x) = s • e x) as bs →
    (RingTheory.Sequence.IsRegular M as ↔ RingTheory.Sequence.IsRegular M₂ bs)