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 lc_tm_of_lc_set_tm_lc_brs_of_lc_set_brs_lc_co_of_lc_set_co_lc_constraint_of_lc_set_constraint_mutual : (forall a1, lc_set_tm a1 -> lc_tm a1) /\ (forall brs1, lc_set_brs brs1 -> lc_brs brs1) /\ (forall g1, lc_set_co g1 -> lc_co g1) /\ (forall phi1, lc_set_constraint phi1 -> lc_constraint phi1).