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_tm_rec_degree_tm_wrt_tm_open_brs_wrt_tm_rec_degree_brs_wrt_tm_open_co_wrt_tm_rec_degree_co_wrt_tm_open_constraint_wrt_tm_rec_degree_constraint_wrt_tm_mutual : (forall a2 a1 n1, degree_tm_wrt_tm n1 a2 -> open_tm_wrt_tm_rec n1 a1 a2 = a2) /\ (forall brs1 a1 n1, degree_brs_wrt_tm n1 brs1 -> open_brs_wrt_tm_rec n1 a1 brs1 = brs1) /\ (forall g1 a1 n1, degree_co_wrt_tm n1 g1 -> open_co_wrt_tm_rec n1 a1 g1 = g1) /\ (forall phi1 a1 n1, degree_constraint_wrt_tm n1 phi1 -> open_constraint_wrt_tm_rec n1 a1 phi1 = phi1).