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 tm_subst_tm_brs_lc_brs : forall brs1 a1 x1, lc_brs brs1 -> lc_tm a1 -> lc_brs (tm_subst_tm_brs a1 x1 brs1).