Hint Extern 1 (lc_co (g_AbsCong _ _ _)) =>
  let x1 := fresh in
  pick_fresh x1;
  apply (lc_g_AbsCong_exists x1).Hint Extern 1 (lc_co (g_CAbsCong _ _ _)) =>
  let c1 := fresh in
  pick_fresh c1;
  apply (lc_g_CAbsCong_exists c1).

Lemma open_co_wrt_co_rec_degree_co_wrt_co : forall g2 g1 n1, degree_co_wrt_co n1 g2 -> open_co_wrt_co_rec n1 g1 g2 = g2.