Hint Resolve lc_set_exp_of_lc_exp : lngen.
(* *********************************************************************** *)
(** * More theorems about [open] and [close] *)
Ltac default_auto ::= auto with lngen; tauto.
Ltac default_autorewrite ::= fail.
(* begin hide *)

Lemma close_exp_wrt_exp_rec_degree_exp_wrt_exp_mutual :
(forall e1 x1 n1,
degree_exp_wrt_exp n1 e1 ->
x1 `notin` fv_exp e1 ->
close_exp_wrt_exp_rec n1 x1 e1 = e1).