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_var : forall a1 g1 c1 c2, c1 <> c2 -> lc_co g1 -> open_tm_wrt_co (co_subst_co_tm g1 c1 a1) (g_Var_f c2) = co_subst_co_tm g1 c1 (open_tm_wrt_co a1 (g_Var_f c2)).