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 co_subst_co_tm_open_tm_wrt_co : forall a1 g1 g2 c1, lc_co g1 -> co_subst_co_tm g1 c1 (open_tm_wrt_co a1 g2) = open_tm_wrt_co (co_subst_co_tm g1 c1 a1) (co_subst_co_co g1 c1 g2).