Hint Immediate degree_exp_wrt_exp_close_exp_wrt_exp_inv : lngen.
(* begin hide *)

(* Specifications: *)
Lemma degree_exp_wrt_exp_open_exp_wrt_exp_rec_mutual :
(forall e1 e2 n1,
degree_exp_wrt_exp (S n1) e1 ->
degree_exp_wrt_exp n1 e2 ->
degree_exp_wrt_exp n1 (open_exp_wrt_exp_rec n1 e2 e1)).
Lemma degree_exp_wrt_exp_open_exp_wrt_exp_rec_mutual :
(forall e1 e2 n1,
degree_exp_wrt_exp (S n1) e1 ->
degree_exp_wrt_exp n1 e2 ->
degree_exp_wrt_exp n1 (open_exp_wrt_exp_rec n1 e2 e1)).