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 eventually_map : forall (f: A->B) (P: infseq A->Prop) (Q: infseq B->Prop), (forall s, P s -> Q (map f s)) -> forall s, eventually P s -> eventually Q (map f s).