(* Now lemmas for interaction of zip with the other primitives *)

Lemma zip_fnd f1 f2 f x (v : V) :
zip f1 f2 = Some f -> fnd x f = Some v ->
exists v1, exists v2,
[/\ zip_f v1 v2 = Some v, fnd x f1 = Some v1 & fnd x f2 = Some v2].