auto.
Qed.

(* Specifications: *)
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').
Lemma Beta_co_subst : forall a a' b x, Beta a a' -> lc_co b -> Beta (co_subst_co_tm b x a) (co_subst_co_tm b x a').