intros. pattern (zip (Cons a sA) (Cons b sB)); rewrite <- recons. simpl. reflexivity.
Qed.
End sec_zip.
Arguments zip [A B] _ _.
Arguments zip_Cons [A B] _ _ _ _.
(* --------------------------------------------------------------------------- *)
(* map and_tl temporal logic *)
Section sec_map_modalop.
Variable A B: Type.

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