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 and_tl_map_conv : forall (f: A->B) (P P': infseq A->Prop) (Q Q': infseq B->Prop), (forall s, Q (map f s) -> P s) -> (forall s, Q' (map f s) -> P' s) -> forall (s: infseq A), (Q /\_ Q') (map f s) -> (P /\_ P') s.