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 consecutive_map_conv : forall (f: A->B) (P: B->B->Prop) (s: infseq A), consecutive P (map f s) -> consecutive (fun x y => P (f x) (f y)) s.