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_unique_lc_brs_unique_lc_co_unique_lc_constraint_unique_mutual : (forall a1 (proof2 proof3 : lc_tm a1), proof2 = proof3) /\ (forall brs1 (proof2 proof3 : lc_brs brs1), proof2 = proof3) /\ (forall g1 (proof2 proof3 : lc_co g1), proof2 = proof3) /\ (forall phi1 (proof2 proof3 : lc_constraint phi1), proof2 = proof3).