induction lsa; inversion 1; intuition; simpl in *;
econstructor.
subst.
trivial.
subst.
trivial.
eauto.
Qed.

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