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

Lemma subst_exp_degree_exp_wrt_exp_mutual : (forall e1 e2 x1 n1, degree_exp_wrt_exp n1 e1 -> degree_exp_wrt_exp n1 e2 -> degree_exp_wrt_exp n1 (subst_exp e2 x1 e1)).