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

Lemma lc_set_exp_of_lc_exp_size_mutual : forall i1, (forall e1, size_exp e1 = i1 -> lc_exp e1 -> lc_set_exp e1).