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_co_spec_rec : forall g1 a1 x1 n1, tm_subst_tm_co a1 x1 g1 = open_co_wrt_tm_rec n1 a1 (close_co_wrt_tm_rec n1 x1 g1).