Hint Extern 1 (lc_exp (abs _)) =>
  let x1 := fresh in
  pick_fresh x1;
  apply (lc_abs_exists x1).

Lemma open_exp_wrt_exp_rec_degree_exp_wrt_exp : forall e2 e1 n1, degree_exp_wrt_exp n1 e2 -> open_exp_wrt_exp_rec n1 e1 e2 = e2.