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 open_tm_wrt_co_rec_degree_tm_wrt_co_open_brs_wrt_co_rec_degree_brs_wrt_co_open_co_wrt_co_rec_degree_co_wrt_co_open_constraint_wrt_co_rec_degree_constraint_wrt_co_mutual : (forall a1 g1 n1, degree_tm_wrt_co n1 a1 -> open_tm_wrt_co_rec n1 g1 a1 = a1) /\ (forall brs1 g1 n1, degree_brs_wrt_co n1 brs1 -> open_brs_wrt_co_rec n1 g1 brs1 = brs1) /\ (forall g2 g1 n1, degree_co_wrt_co n1 g2 -> open_co_wrt_co_rec n1 g1 g2 = g2) /\ (forall phi1 g1 n1, degree_constraint_wrt_co n1 phi1 -> open_constraint_wrt_co_rec n1 g1 phi1 = phi1).