induction 1; intuition; simpl in *.
econstructor.
inversion H1; clear H1; subst.
econstructor.
intuition.
eauto.
Qed.

Theorem list_pred_combine_l :
forall (A B C : Set)P1 P2 (lsa : list A)(lsb : list B)(lsc : list C),
list_pred P1 lsa lsc ->
list_pred P2 lsb lsc ->
list_pred (fun p c => P1 (fst p) c /\ P2 (snd p) c) (combine lsa lsb) lsc.