Set Bullet Behavior "Strict Subproofs".
Set Implicit Arguments.
Require Export FcEtt.tactics.
Require Export FcEtt.imports.
Require Export FcEtt.ett_inf.
Require Export FcEtt.ett_ott.
Require Export FcEtt.ett_ind.
Require Export FcEtt.ext_context_fv.
Require Export FcEtt.toplevel.
intros.  induction H; auto.
eapply Value_lc in H. eauto.
Qed.
intros.  induction H; auto.
- 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.
intros. f_equal.
auto.
Qed.

Lemma Beta_tm_subst : forall a a' b x, Beta a a' -> lc_tm b -> Beta (tm_subst_tm_tm b x a) (tm_subst_tm_tm b x a').