Hint Resolvegt_Sn_Ogt_Sn_ngt_n_S : arith. Hint Immediategt_S_ngt_pred : arith. Hint Resolvegt_irreflgt_asym : arith. Hint Resolvele_not_gtgt_not_le : arith. Hint Immediatele_S_gtgt_S_le : arith. Hint Resolvegt_le_Sle_gt_S : arith. Hint Resolvegt_trans_Sle_gt_transgt_le_trans: arith. Hint Resolveplus_gt_compat_l: arith.