do 3 intro.
destruct (In_map_inv H0).
destruct H1.
subst...
Qed.

(* Specifications: *)
Lemma incl_in T (a b: list T): incl a b -> forall x, In x a -> In x b.
Lemma length_excl_counts X (p: X -> bool) (l: list X):
length l = count p l + count (negb ∘ p) l.