Hint Immediate degree_exp_wrt_exp_open_exp_wrt_exp_inv : lngen.
(* *********************************************************************** *)
(** * Theorems about [open] and [close] *)
Ltac default_auto ::= auto with lngen brute_force; tauto.
Ltac default_autorewrite ::= fail.
(* begin hide *)

Lemma close_exp_wrt_exp_rec_inj_mutual :
(forall e1 e2 x1 n1,
close_exp_wrt_exp_rec n1 x1 e1 = close_exp_wrt_exp_rec n1 x1 e2 ->
e1 = e2).