induction lsa; destruct lsb; intuition; simpl in *.
f_equal; eauto.
Qed.

(* Specifications: *)
Theorem map_ext_pred :
forall (A B C : Set)(P : A -> B -> Prop)(lsa : list A)(lsb : list B)(f1 : A -> C)(f2 : B -> C),
list_pred P lsa lsb ->
(forall a b, P a b -> (f1 a) = (f2 b)) ->
map f1 lsa = map f2 lsb.