Hint Resolve lc_exp_of_degree : lngen.
Ltac typ_lc_exists_tac :=
repeat (match goal with
| H : _ |- _ =>
fail 1
end).
Ltac exp_lc_exists_tac :=
repeat (match goal with
| H : _ |- _ =>
let J1 := fresh in pose proof H as J1; apply degree_exp_wrt_exp_of_lc_exp in J1; clear H
end).

Lemma lc_abs_exists :
forall x1 e1,
lc_exp (open_exp_wrt_exp e1 (var_f x1)) ->
lc_exp (abs e1).