Hint Immediate degree_exp_wrt_exp_close_exp_wrt_exp_rec_inv : lngen.
(* end hide *)

(* Specifications: *)
Lemma degree_exp_wrt_exp_close_exp_wrt_exp_inv :
forall e1 x1,
degree_exp_wrt_exp 1 (close_exp_wrt_exp x1 e1) ->
degree_exp_wrt_exp 0 e1.
Lemma degree_exp_wrt_exp_close_exp_wrt_exp_inv :
forall e1 x1,
degree_exp_wrt_exp 1 (close_exp_wrt_exp x1 e1) ->
degree_exp_wrt_exp 0 e1.