induction 1; intuition; simpl in *.
f_equal; intuition.
Qed.

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