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_constraint_spec_rec : forall phi1 g1 c1 n1, co_subst_co_constraint g1 c1 phi1 = open_constraint_wrt_co_rec n1 g1 (close_constraint_wrt_co_rec n1 c1 phi1).