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_brs_wrt_tm_rec_degree_brs_wrt_tm : forall brs1 a1 n1, degree_brs_wrt_tm n1 brs1 -> open_brs_wrt_tm_rec n1 a1 brs1 = brs1.