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 lc_body_brs_wrt_tm : forall brs1 a1, body_brs_wrt_tm brs1 -> lc_tm a1 -> lc_brs (open_brs_wrt_tm brs1 a1).