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_tm_degree_tm_wrt_co_tm_subst_tm_brs_degree_brs_wrt_co_tm_subst_tm_co_degree_co_wrt_co_tm_subst_tm_constraint_degree_constraint_wrt_co_mutual : (forall a1 a2 x1 n1, degree_tm_wrt_co n1 a1 -> degree_tm_wrt_co n1 a2 -> degree_tm_wrt_co n1 (tm_subst_tm_tm a2 x1 a1)) /\ (forall brs1 a1 x1 n1, degree_brs_wrt_co n1 brs1 -> degree_tm_wrt_co n1 a1 -> degree_brs_wrt_co n1 (tm_subst_tm_brs a1 x1 brs1)) /\ (forall g1 a1 x1 n1, degree_co_wrt_co n1 g1 -> degree_tm_wrt_co n1 a1 -> degree_co_wrt_co n1 (tm_subst_tm_co a1 x1 g1)) /\ (forall phi1 a1 x1 n1, degree_constraint_wrt_co n1 phi1 -> degree_tm_wrt_co n1 a1 -> degree_constraint_wrt_co n1 (tm_subst_tm_constraint a1 x1 phi1)).