induction lsb; inversion 1; intuition; subst; simpl in *;
econstructor.
inversion H; clear H; subst.
trivial.
inversion H; clear H; subst.
eauto.
Qed.

(* Specifications: *)
Lemma list_pred_map_r'
: forall (A B C : Set) (lsa : list A) (lsb : list B) (P : A -> C -> Prop) (f : B -> C),
list_pred (fun a b => P a (f b)) lsa lsb ->
list_pred P lsa (map f lsb).