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 weak_until_map_conv : forall (f: A->B) (J P: infseq A->Prop) (K Q: infseq B->Prop), (forall s, K (map f s) -> J s) -> (forall s, Q (map f s) -> P s) -> forall (s: infseq A), weak_until K Q (map f s) -> weak_until J P s.