(* The converse seems to require much more work *)

Definition fstAB := fst (A:=A) (B:=B).

Lemma exteq_zip_map : forall (f: A->B) (sA: infseq A) (sB: infseq B), always (now (fun c: A*B => let (x, y) := c in y = f x)) (zip sA sB) -> exteq sB (map f (map fstAB (zip sA (map f sA)))).