- inversion H. apply lc_body_tm_wrt_tm; auto.
- apply Value_lc in H. inversion H.
apply lc_body_tm_wrt_tm; auto.
- inversion H. apply lc_body_tm_wrt_co; auto.
- apply Toplevel_lc in H. inversion H. auto.
Qed.

(* Specifications: *)
Lemma cf : forall A B (f : A -> B) (a b : A),  a = b -> f a = f b.
intros. f_equal.