induction ls; intuition; simpl in *.
econstructor.
inversion H; clear H; subst.
econstructor.
intuition.
eapply H3.
eapply In_gen_weaken; eauto.
eauto.
Qed.

Theorem In_gen_zip_fst :
forall (A B : Set)(ea : A -> A -> Prop)(lsa : list A)(lsb : list B) a b,
In_gen (fun a b => ea (fst a) (fst b)) (a, b) (zip lsa lsb) ->
In_gen ea a lsa.