Hint Resolvegt_Sn_Ogt_Sn_ngt_n_S : arithv62. Hint Immediategt_S_ngt_pred : arithv62. Hint Resolvegt_irreflgt_asym : arithv62. Hint Resolvele_not_gtgt_not_le : arithv62. Hint Immediatele_S_gtgt_S_le : arithv62. Hint Resolvegt_le_Sle_gt_S : arithv62. Hint Resolvegt_trans_Sle_gt_transgt_le_trans: arithv62. Hint Resolveplus_gt_compat_l: arithv62.