CoFixpoint zip (sA: infseq A) (sB: infseq B) : infseq (A*B) := 
  match sA, sB with
    | Cons a sA0, Cons b sB0 => Cons (a, b) (zip sA0 sB0)
  end.

Lemma impl_tl_map : forall (f: A->B) (P P': infseq A->Prop) (Q Q': infseq B->Prop), (forall s, Q (map f s) -> P s) -> (forall s, P' s -> Q' (map f s)) -> forall (s: infseq A), (P ->_ P') s -> (Q ->_ Q') (map f s).